1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 1

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 2

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 3

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 4

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 5

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 6

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 7

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 8

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 9

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 10

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 11

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 12

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

eSolutions Manual - Powered by Cognero Page 13

4-5 Compute with Scientific Notation

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

1. About 1 × 106 fruit flies weigh 1.3 × 10

2 pounds.

How much does one fruit fly weigh? Write in scientific notation.

SOLUTION: Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly.

One fruit fly weighs about 1.3 × 10–4

pounds.

ANSWER:

about 1.3 × 10–4

lbs

Evaluate each expression. Express the result inscientific notation.

2. (1.217 × 105) – (5.25 × 10

4)

SOLUTION: To subtract the numbers, rewrite them so that they

have the same power of 10. Write 1.217 × 105 as

12.17 × 104. Use the distributive property to group

the factors. Then subtract 5.25 from 12.17. Write thefinal answer in scientific notation.

ANSWER:

6.92 × 104

3. (2.003 × 104) + (7.98 × 10

7)

SOLUTION: To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 7.98 ×

107 as 7980 × 10

4. Use the distributive property to

group the factors. Then add 2.003 and 7980. Write the final answer in scientific notation.

ANSWER:

7.982003 × 107

4.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 8.25 by 2.75. Subtract the exponents.

ANSWER:

3 × 106

5. (3.45 × 107) – (24,650,000)

SOLUTION: Write 24,650,000 in scientific notation.

24,650,000 = 2.465 × 107

To subtract the numbers, use the distributive propertyto group the factors. Then subtract 2.465 from 3.45. Write the final answer in scientific notation.

ANSWER:

9.85 × 106

6. 523 + (6.2 × 103)

SOLUTION: Write 523 in scientific notation.

523 = 5.23 × 102

To add the numbers, rewrite one addend so that both

addends have the same power of 10. Write 6.2 × 103

as 62 × 102. Use the distributive property to group

the factors. Then add 5.23 and 62. Write the final answer in scientific notation.

ANSWER:

6.723 × 103

7.

SOLUTION: Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents.

ANSWER:

2.2 × 10–2

8. The equatorial circumference of Earth is about 4 ×

104 kilometers. The equatorial circumference of

Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter’s circumference than Earth’s?

SOLUTION: Estimate the equatorial circumference of Jupiter and write in scientific notation.

439,263.8 ≈ 400,000 or 4 × 105

Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth.

So, Jupiter's circumference is about 10 times greater than Earth's circumference.

ANSWER: about 10 times greater

9. The United States has the most miles of roads in the

world at about 4 × 106 miles. Japan has about 7.3 ×

105 miles. How many more miles of roads does the

United States have than Japan? Write in scientific notation.

SOLUTION: Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United Stateshave than Japan.

So, the United States has 3.27 × 106 more miles of

roads than Japan.

ANSWER:

about 3.27 × 106 mi

10. The speed of light is about 1.9 × 105 miles per

second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation.

SOLUTION: Write 500 in scientific notation.

500 = 5 × 102

Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun.

The distance between the Earth and the sun is about

9.5 × 107 miles.

ANSWER:

about 9.5 × 107 mi

Evaluate each expression. Express the result inscientific notation.

11. (5.32 × 108)(3.54 × 10

3)

SOLUTION:

ANSWER:

1.88328 × 1012

12. (1.48 × 10–5)(6.5 × 10

–6)

SOLUTION:

ANSWER:

9.62 × 10–11

13. (9.5 × 10–4

)(28,400)

SOLUTION:

ANSWER:

2.698 × 101

14. (0.042)(3.15 × 104)

SOLUTION:

ANSWER:

1.323 × 103

15.

SOLUTION:

ANSWER:

7 × 1013

16.

SOLUTION:

ANSWER:

6 × 1011

17.

SOLUTION:

ANSWER:

1.25 × 107

18.

SOLUTION:

ANSWER:

1.99 × 102

19. (3.205 × 103) + (5.83 × 10

5)

SOLUTION:

ANSWER:

5.86205 × 105

20. 6,263,000 + (5.4 × 108)

SOLUTION:

ANSWER:

5.46263 × 108

21. (2.764 × 108) – (6.2 × 10

7)

SOLUTION:

ANSWER:

2.144 × 108

22. (9.518 × 107) – 22,000

SOLUTION:

ANSWER:

9.5158 × 107

23. (4.21 × 10–3

)(56,200)

SOLUTION:

ANSWER:

2.36602 × 102

24. (8.08 × 106)(3.34 × 10

3)

SOLUTION:

ANSWER:

2.69872 × 1010

25. (7.57 × 102)(1.10 × 10

5)

SOLUTION:

ANSWER:

8.327 × 107

26. (0.0159)(5.19 × 10–3

)

SOLUTION:

ANSWER:

8.2521 × 10–5

27. The diameter of Mars is about 7 × 106 meters. A

standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball?

SOLUTION: Write 0.04 in scientific notation.

0.04 = 4 × 10–2

Divide the diameter of Mars by the diameter of a table tennis ball.

The diameter of Mars is about 1.75 × 108 times greater than that of a table tennis ball.

ANSWER:

about 1.75 × 108 times greater

28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island isthe smallest state with an area (including water) of

about 4 × 103 square kilometers. About how many

times greater is the area of the United States than the area of Rhode Island?

SOLUTION: Estimate the total area of the United States and writein scientific notation.

9,826,630 ≈ 10,000,000 or 1 × 107

Divide the area of the United States by the area of Rhode Island.

The area of the United States is about 2.5 × 103 or

2500 times greater than the area of Rhode Island.

ANSWER: about 2500 times greater

29. The Earth is 1.55 × 108 kilometers from the Sun.

Mercury is 5.80 × 107 kilometers from the Sun. Find

the difference in distances and express your answer in scientific notation.

SOLUTION: To find the difference in distances, subtract the numbers.

ANSWER:

9.7 × 107 km

30. Each minute, there are approximately 6 × 103 flashes

of lightning around the world. The air around a

lightning bolt is heated to about 5.4 × 104 degrees

Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in aday? b. About how hot is the sun in degrees Fahrenheit?

SOLUTION: a. There are 1440 minutes in a day. Write 1440 in scientific notation.

1440 = 1.44 × 103

To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day.

There are 8.64 × 106

or 8,640,000 flashes of lightning

in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5.

In degrees Fahrenheit, the temperature of the sun is

1.08 × 104 or 10,800.

ANSWER:

a. 8.64 × 106; 8,640,000

b. 1.08 × 104; 10,800

31. A music website recently announced that over 4 ×

109 songs have been downloaded. It also announced

that it has 5 × 107 registered users. Find the average

number of downloads per user and express your answer in scientific notation.

SOLUTION: To find the average number of downloads per user, divide the number of songs by the number of users.

ANSWER:

8 × 101 downloads

32. Use Math Tools The table shows the weights of various marine and land animals.

a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standardform.

SOLUTION: a. Estimate the weight of the right whale.

8.82 × 104 ≈ 8 × 10

4

Divide the weight of the right whale by 10.

8 × 103

is close to the weight of the white rhinoceros.The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant.

The blue whale is about 2 × 101 or 20 times heavier

than the African elephant. c. Add the weights of the fin whale, right whale, and white rhinoceros.

The estimated combined weight of the fin whale,

right whale, and white rhinoceros is 2.0 × 105 or

200,000 pounds.

ANSWER: a. white rhinoceros b. 20 times

c. 2.0 × 105; 200,000

33. The average width of a human hair is 4 × 10–3

centimeter. If the cross section of the average hair is

round, use the formula A = 3.14r2 to find the

approximate area of the cross section of a hair. Write your answer in scientific notation.

SOLUTION: The width of a human hair is equal to twice the

radius. So, the radius of a human hair is 2 × 10–3

centimeter. Substitute 2 × 10–3

for r in the formula A

= 3.14r2.

The area of the cross section of a hair is 1.256 × 10–

5 cm

2.

ANSWER:

1.256 × 10–5

cm2

34. A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using

1.6 × 103 cubic feet of sand that weighs 95 pounds

per cubic foot and 1.25 × 103 cubic feet of sand that

weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court?

SOLUTION: To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feetof each type of sand by its weight per cubic foot. Find the sum of these products.

2.62 × 105

pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number ofpounds by 2000. Write 2000 in scientific notation.

2000 = 2 × 103

1.31 × 102

or 131 tons of sand are being used for the volleyball court.

ANSWER: 131 tons

Evaluate each expression. Express the result inscientific notation.

35.

SOLUTION:

ANSWER:

1 × 10–1

36.

SOLUTION:

ANSWER:

1.44 × 1022

37.

SOLUTION:

ANSWER:

6.54 × 1011

38.

SOLUTION:

ANSWER:

2.94 × 103

39.

SOLUTION:

ANSWER:

8.88 × 10–25

40.

SOLUTION:

ANSWER:

3.24 × 10–1

41. (8.2 × 104 + 8,249) × 10

8

SOLUTION:

ANSWER:

9.0249 × 1012

42. (5.29 × 104 – 52,000) × 10

5

SOLUTION:

ANSWER:

9 × 107

43. Identify Structure Write an addition expression anda subtraction expression, each with a value of 2.4 ×

10–3

.

SOLUTION: Sample answers:

ANSWER:

Sample answers: (2.15 × 10–3) + (2.5 × 10–4); (2.56

× 10–3

) – (1.6 × 10–4

)

44. Which One Doesn’t Belong? Identify the expression that does not belong with the other three. Explain your reasoning.

SOLUTION:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

ANSWER:

52.5 × 108 does not belong. 52.5 × 108 = 5.25 × 109,

while the three remaining expressions each

equal 5.25 × 107.

45. Persevere with Problems There are about 2.5 ×

1010

red blood cells in the average adult. A googol is

1 × 10100

. About how many adults would it take to have a total of 1 googol red blood cells?

SOLUTION: To find how many adults it would take to have a totalof 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult.

It would take about 4 × 1089

adults to have a total of 1 googol red blood cells.

ANSWER:

about 4 × 1089

adults

46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers?

SOLUTION: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

ANSWER: Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing.

47. Ariana is evaluating (8 × 103) + (4 × 105), as shown

below.

What should Ariana have done differently to evaluatethe expression correctly?

A made both numbers have the same power of 10

B subtracted the exponentsC multiplied 8 × 4 instead of adding 8 + 4

D made the last line 12 × 108

SOLUTION: She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer.

ANSWER: A

48. What is the value of (2.8 × 103)(1,600,000)?

F 4.48 × 1018

G 4.48 × 106

H 44.8 × 109

J 4.48 × 109

SOLUTION:

Choice J is the correct answer.

ANSWER: J

49. After its first year in business, a movie Web site announced that over 500,000,000 movies were

downloaded by 4 × 106 registered users. What is the

average number of movies per user?

A about 1.25 × 10–25 movies

B about 125 movies

C 1.25 × 103 movies

D about 12.5 movies

SOLUTION: To find the average number of movies per user, divide the number of movies downloaded by the number of users.

The average number of movies per user is 1.25 × 103

or 125. Choice B is the correct answer.

ANSWER: B

50. Short Response Earth is 1.55 × 108 kilometers

from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation.

SOLUTION:

The difference in distances is 4.6 × 107

kilometers.

ANSWER:

4.6 × 107 km

Write an integer for each situation. Then identify its opposite.

51. 58°C below zero

SOLUTION: Because it is below zero, the integer is –58. Its opposite is +58 or 58.

ANSWER: –58; +58 or 58

52. 15 gallons per mile more than usual

SOLUTION: Because it is more than normal, the integer is +15 or 15. Its opposite is –15.

ANSWER: +15 or 15; –15

53. a withdrawl of $4500

SOLUTION: Because it is a withdrawl, the integer is –4500. Its opposite is +4500 or 4500.

ANSWER: –4500; +4500 or 4500

54. a scuba diver's descent of 50 feet

SOLUTION: Because it is a descent, the integer is –50. Its opposite is +50 or 50.

ANSWER: –50; +50 or 50

55. a bank deposit of $68.00

SOLUTION: Because it is a deposit, the integer is +68 or 68. Its opposite is –68.

ANSWER: +68 or 68; –68

56. an airplane's ascent of 300 feet

SOLUTION: Because it is an ascent, the integer is +300 or 300. Its opposite is –300.

ANSWER: +300 or 300; –300

Complete each expression.57. 18 – 5 = 18 + _

SOLUTION: 18 – 5 = 18 + (–5)

ANSWER: –5

58. _ – (–3) = 12

SOLUTION: 9 – (–3) = 12

ANSWER: 9

59. 12 = 10 – _

SOLUTION: 12 = 10 – (–2)

ANSWER: –2

60. The volume of one cube is 53 cubic inches. What is

the volume of 3.5 of these cubes?

SOLUTION: To find the volume of 3.5 of these cubes, multiply thevolume of one cube by 3.5.

The volume of 3.5 of these cubes is 437.5 cubic inches.

ANSWER:

437.5 in3

61. The speed of sound is approximately 7.6 × 102 miles

per hour. Write 7.6 × 102 in standard form.

SOLUTION:

7.6 × 102 = 760

ANSWER: 760

62. The SR-71 Blackbird is more than 30 years old. It

can fly at altitudes above 8 × 104 feet. Is it more

appropriate to report the altitude as 8 × 104 feet or as

9.6 × 105 inches?

SOLUTION:

The measure 8 × 104 feet is more appropriate. The

number is very large so choosing a larger unit of measure is more meaningful.

ANSWER:

8 × 104 ft

Determine whether each equation is true or false . If the equation is false , explain why.

63. 3 × (–4) = –12

SOLUTION: This statement is true. The product of two integers with different signs is negative.

ANSWER: true

64.

SOLUTION: This statement is false.

ANSWER:

false;

65. –15 ÷ (–3) = 5

SOLUTION: This statement is true. The quotient of two integers with the same sign is positive.

ANSWER: true

66. –36 ÷ 6 = 6

SOLUTION: This statement is false. The quotient of two integers with different signs is negative. –36 ÷ (6) = –6

ANSWER: false; –36 ÷ (6) = –6

67. –12 × (–11) = 132

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

68. –1 × (–1) = 1

SOLUTION: This statement is true. The product of two integers with the same sign is positive.

ANSWER: true

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4-5 Compute with Scientific Notation