Scientific Notation

A short-hand way of writinglarge numbers without writing all of the zeros.

The Distance From the Sun to the Earth

93,000,000 miles

Step 1

Move decimal left

Leave only one significant number in front of the decimal

Step 2

Write number without zeros

Step 3

Count how many places you moved decimalMake that your power of tenThe power of ten is the letter “E” (exponential) for your calculators.

The power often is 7 becausethe decimalmoved 7 places.

93,000,000 - Standard Form

9.3 x 107 - Scientific Notation

4567 x 10-5 -

Scientific Notation

.04567 -

Standard Form

What if it has a decimal?

Move the decimal to the right after the first significant (not a zero) number.

.000,000,043 --- Standard Form

4.3 x 10-8 - Scientific Notation

Practice Problems

1.) 9.85 x 10-4? =

2.) 64,100,000,000 =

3.) 2.79 x 10-6 =

4.) 431,200,000 =

5.) .000,0496=

1) .000,985

2) 6.41 x1010

3) .000,00279

4) 4.31 x 108

5) 4.96 x 10-5

Write in scientific notation or standard form.

More Practice Problems

1) 734,000,000 = ______ x 108

2) .000,000,000,870 = ______x 10-10

3) 90,000,000,000 = _____ x 1010

On these, decide where the decimal will be moved.

1)7.34 x 108

2) 8.70 x 10-103) 9.0 x 1010

Complete Practice Problems

1) 50,000

2) 7,200,000

3) .000,000,802

Write in scientific notation .

1) 5.0 x 1042) 7.2 x 106 3) 8.02 x 10-7

Scientific Notation to Standard Form

Move the decimal to the right

3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Write in Standard Form

6.27 x 106

9.01 x 104

4.603 x 108

9.94 x 102

6,270,000

90,100

460,300,000

994

Write in Scientific Notation

3.89 x 10-7

3.872 x 10-6

8.940 x 10-3

4.931 x 10-3

23.8761 x 10-4

.000,000,389

.000,003,872

.00894

.004931

.00238761

Write in Scientific Notation1. 0.07882 =2. 0.000,00272338 =3. 118000 =4. 87200 =5. 0.000,02786 =6. 0.000,000664 =7. 450 =8. 74171.7 =9. 770 =10. 0.000,0085 =

1. 7.882 × 10-2

2. 2.72338 × 10-63. 1.18 × 105

4. 8.72 × 104

5. 2.786 × 10-5

6. 6.64 × 10-7

7. 4.5 × 102

8. 7.41717 × 104

9. 7.7 × 102

10. 8.5 × 10-6

1. What is this number in standard form? 6.73 x 10-6

6730

000

.000

0067

3

.000

0673

6730

00

0% 0%

50%50%A. 6,730,000

B. 0.00000673

C. 0.0000673

D. 673,000

2. When the exponent is positive you move the decimal to the:

Lef

t

Rig

ht T

op

botto

m

11%6%

0%

83%A. Left

B. Right

C. Top

D. bottom

3. What does your calculator use to designate as a power of ten for scientific notation

10 P G E

11%

78%

11%

0%

A. 10

B. P

C. G

D. E

4. Why is scientific notation important when dealing with astronomy?

They

wan

t to

They

are

real

l...

Pla

nets

and s

t...

It h

elps

with

...

0%7%

80%

13%

A. They want to

B. They are really big numbers and they are lazy

C. Planets and stars are really far away so using scientific notation makes it easier to record the numbers

D. It helps with Inverse Square Law

5. Which of these numbers shows 1 million in scientific notation?

1 x

103

1 x

104

1 x

107

1 x

106

0%

56%

44%

0%

A. 1 x 103

B. 1 x 104

C. 1 x 107

D. 1 x 106

6. Changer 1204.6 in scientific notation?

1.2

x 1

03

120

x 1

0-2

12

x 10

2

120

4 x

100

79%

14%7%

0%

A. 1.2 x 103

B. 120 x 10-2

C. 12 x 102

D. 1204 x 100

7. Change 17.8 in scientific notation?

1.7

8 x

102

1.7

8 x

101

1.7

8 x

10-1

1.7

8 x

10-2

17%

0%

11%

72%A. 1.78 x 102

B. 1.78 x 101

C. 1.78 x 10-1

D. 1.78 x 10-2

8. Change 567,310 in scientific notation?

567

x 1

03

56.

7 x

105

5.6

7310

x 1

05

5 x

106

22%

0%

67%

11%

A. 567 x 103

B. 56.7 x 105

C. 5.67310 x 105

D. 5 x 106

9. Convert 8.36 x 102 in scientific notation?

8360

083

60 836

8360

00

17%

0%

78%

6%

A. 83600

B. 8360

C. 836

D. 836000

10. Convert 9.16 x 106 in scientific notation?

.000

0009

16

.000

916

9160

9160

000

6%

94%

0%0%

A. 0.000000916

B. 0.000916

C. 9,160

D. 9,160,000