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Objective
Find the product of decimals and whole numbers
Vocabulary
Scientific notation
A way of expressing a number as the product of a number that is at least 1 but less than 10
and the power of 10
Example 1 Multiply Decimals
Example 2 Multiply Decimals
Example 3 Annex Zeros in the Product
Example 4 Annex Zeros in the Product
Example 5 Scientific Notation
1/5
Find 18.9 4
Write the problem vertically line up digits, not place value
Multiply 4 9 = 36
Put the one’s place value of 6 under the 4
Carry the ten’s place value of 3
3
Multiply 4 8 = 32
Add the carry of 3 to 32 = 35
Put the one’s place value of 5 under the 8
Carry the ten’s place value of 3
3
1/5
Find 18.9 4Multiply 4 1 = 4
3 Add the carry of 3 to 4 = 7
Put the one’s place value of 7 under the 1
Count the decimal places in 18.9
31
Count the decimal places in 4
0
Add the place values 1 + 0
1
Beginning on the right of the 6, place a decimal 1 place to the leftAnswer: 75.6
Answer: 100.8
1/5
Find 12.6 8
4
2/5
Find 0.56 7
Write the problem vertically line up digits, not place value
Multiply 7 6 = 42
Put the one’s place value of 2 under the 7
Carry the ten’s place value of 4
Multiply 7 5 = 35
Add the carry of 4 to 35 = 39
Put the one’s place value of 9 under the 5
Carry the ten’s place value of 3
3
4
2/5
Find 0.56 7Multiply 7 0 = 0
Add the carry of 3 to 0 = 3
Put the one’s place value of 3 under the 0
3
Count the decimal places in 0.56
2
Count the decimal places in 7
0
Add the place values 2 + 0Beginning on the right of the 2, place a decimal 2 places to the leftAnswer: 3.92
2
Answer: 3.32
2/5
Find 0.83 4
3/5
1Find 3 0.016
Write the problem vertically line up digits, not place value
Since 0.016 has more digits than 3, put it on top
Multiply 3 6 = 18Put the one’s place value of 8 under the 3Carry the ten’s place value of 1Multiply 3 1 = 3Add the carry of 1 to 3 = 4Put the one’s place value of 4 under the 1
3/5
1
Find 3 0.016
Multiply 3 0 = 0
Put the one’s place value of 0 under the 0 next to the 1
Multiply 3 0 = 0
Put the one’s place value of 0 under the 0
Count the decimal places in 0.016
3
Count the decimal places in 3
0
Add the place values 3 + 0
3
Beginning on the right of the 8, place a decimal 3 places to the left
Answer: 0.048
Answer: 0.092
3/5
Find 4 0.023
ALGEBRA Evaluate
4/5
Write the algebraic expression5g
Remember: 5g means 5 g
Replace g with 0.0091
Bring down the 5
5 (0.0091)
Write the problem vertically line up digits, not place value
Since 0.091 has more digits than 5, put it on top
0.0091x 5
ALGEBRA Evaluate
4/5
0.0091x 5
Multiply 5 1 = 5
Put the one’s place value of 5 under the 5
5Multiply 5 9 = 45Put the one’s place value of 5 under the 9Carry the ten’s place value of 4
4
5
ALGEBRA Evaluate
4/5
0.0091x 5
Multiply 5 0 = 0
5Multiply 5 0 = 0
Put the one’s place value of 4 under the 0 next to the 9
4
5
Add the carry of 4 to 0 = 4
Put the one’s place value of 0 under the 0
40
Multiply 5 0 = 0Put the one’s place value of 0 under the 0
0
ALGEBRA Evaluate
4/5
0.0091x 5
0 0455
4 Count the decimal places in 0.0914 Count the decimal places in 50
Add the place values 4 + 0
Beginning on the right of the 5, place a decimal 4 places to the left
.
Answer: 0.0455
4
ALGEBRA Evaluate
Answer: 0.0186
4/5
ASTRONOMY The average distance from Earth to the Sun is 1.5 108 kilometers. Write this distance in standard form.
5/5
Write the problem1.5 108 Use the calculatorPut 1.5 in calculator
1.5
Push the sign
Put 10 in calculator
10
Push the exponent key [yx]
yx
ASTRONOMY The average distance from Earth to the Sun is 1.5 108 kilometers. Write this distance in standard form.
5/5
1.5 108
1.5 10 yx
Put the exponent 8 in calculator
8 Push the = sign
=
150,000,000 Make sure to add the commas in the appropriate places
Answer: The average distance is 150,000,000 kilometers
Answer: 240,000 years
ARCHAEOLOGY An archaeologist claims that a particular artifact is 2.4 105 years old. Write this age in standard form.
*
5/5
Assignment Lesson 4:1 Multiplying Decimals 15 - 38 All
by Whole Numbers