Scientific Notation

CCA Answers

• 1. D• 2.• 3. B• 4. A• 5. B• 6. C• 7. A• 8. A• 9. C• 10. D• 11. A

• 12. C• 13. B• 14. B• 15. C• 16. A• 17. $238.22• 18. $7.98• 19. D• 20. C• 21. D• Bonus: D (6 2/3)

Exponents

25

Base

Exponent

It means 2 · 2 · 2 · 2 · 2

Look at the back of your worksheetWrite in exponential form.11. 18 · 18 · 18

12. 2a · 2a · 2a

13. (-9)(-9)(-9)(-9)

14. Is -24 = (-2)4? Why or why not?

Evaluate:15. 102

16. 101

17. 100

18. 10-1

19. 10-2

Scientific Notation

• Scientific Notation is used to write very large or very small numbers in a way that is easier to read and understand

• 2.34 x 105 is in scientific notation.• The first number has to be one or greater, but less

than 10.• It will always be times 10 to the something power. • The exponent tells you how many times the

decimal has been moved.

Really Large Numbers

• When a number starts out as a number greater than one, the exponent will be positive.

• 4,250,000,000• 4.25 x 109

• 5.8 x 104

• 58,000

Really Small Numbers

• When a number starts out less than one, the exponent will be negative.

• 0.000456 • 4.56 x 10-6

• 3.974 x 10-7

• 0.0000003974

Examples

• Which are in scientific notation?3.5 x 103

62.6 x 10-2

0.86 x 108

3.82 x 100-6 4.6 x 100

• Yes• No• No• No• Yes

Examples

• Write in scientific notation

• 13,030,000• 0.000 092• 0.003 5• 4,825,000,000• 675 million• 283 hundred

thousandths

• 1.303 x 107

• 9.2 x 10-5

• 3.5 x 10-3

• 4.825 x 109

• 6.75 x 108

• 2.83 x 10-3

Examples

• Write as a standard number:

• 3.84 x 106

• 6.2 x 10-5

• 5 x 10-3

• 1.2345 x 1010

• 7.91 x 100

• 5 x (7 x 106)

• 3,840,000• 0.000 062• 0.005• 12,345,000,000• 7.91• 35,000,000

Front of Worksheet1. The distance from Earth to the moon is about 3.8 · 105 kilometers. Which

is another way to express this distance?A. 3,800 kmB. 38,000 kmC. 380,000 kmD. 3,800,000 km

2. The width of a plant cell is approximately 0.000183 meters. How is the expressed in scientific notation?

F. 1.83 · 10-5 mG. 1.83 · 10-4 mH. 18.3 · 10-4 mJ. 183 · 10-5 m

3. The United States produces 4.543 · 106 tons of solid waste annually. This number can be written as—

A. 454,300B. 4,543,000C. 45,430,000D. 4,543,000,000

4. The proteins in your body are made up of amino acids. An amino acid is about 0.000000008 meters wide. How is this number expressed in scientific notation?

F. 8 · 108

G. 8 · 10-8

H. 8 · 109

J. 8 · 10-9

10. The diameter of an oxygen molecule is about 0.000000000339 meters. What is the diameter of two oxygen molecules lined up in a row expressed in scientific notation?

F. 6.78 · 10-9 G. 6.78 · 10-10 mH. 6.78 · 10-10 mJ. 678 · 10-8 m