Worksheet on Powers of Ten and Scientific Notation

Scientific Notation is used a lot in astronomy. It helps us to write succinctly the very large and small numbers we often encounter (sizes, distances, times, etc). The appendix of Bennett gives a nice overview of Scientific Notation. Be sure to read the section on Powers of Ten immediately preceeding it -- it is the basis of Scientific Notation.

I. Powers of Ten worksheet:

Express the following powers of ten in "normal notation", for example 1000:

1) 10⁴ =

2) 10⁷ =

3) 10¹⁷ =

4) 10^-1 =

5) 10^-4 =

6) 10^-12 =

Express the following numbers as powers of ten.

7) 10 =

8) 100,000 =

9) 1,000,000,000,000,000,000 =

10) 0.001 =

11) 1 =

12) 0.000000001 =

13) Why is this notation useful?

ANSWERS:

1) 10,000

2) 10,000,000

3) 100,000,000,000,000,000

4) 0.1

5) 0.0001

6) 0.000000000001

7) 10¹

8) 10⁵

9) 10¹⁸

10) 10^-3

11) 10⁰

12) 10^-9

13) You can read and write large numbers much more easily.

II. Scientific Notation worksheet:

Convert the following numbers to Scientific Notation:

14) 5,213 =

15) 73,200 =

16) 23.21 =

17) 21,000,000,000 =

18) 4,713,000,000 =

19) 0.02 =

20) 0.000314 =

21) 0.00000000043791

Convert the following numbers to "normal notation" (eg, 1000)"

22) 2 x 10³ =

23) 2.331 x 10⁵ =

24) 9.51 x 10²² =

25) 5 x 10^-3 =

26) 7.6278 x 10^-5 =

27) 10³ + 10⁵ =

28) (2.51 x 10² ) + (5.23 x 10⁴ ) =

29) 10⁴ - 10² =

30) (2 x 10⁴ ) - (7 x 10² ) =

31) 10¹² x 10⁵ =

32) (7.2 x 10⁵ ) x (2.12 x 10^-2 ) =

33) 10⁹ / 10⁴ =

34) (2.3 x 10⁷) / (9.2 x 10²) =

** If you have any questions, please visit me during office hours (ormake an appointment) and we can go through them point-by-point.

** If you want help learning how to type these numbers into your calculator, see me (each calculator is different).

** REMEMBER: when you look at a number in scientific notation:

• The power of ten tells you ROUGHLY how big the number is (eg, 10³ , 10⁸ , or 10^-5).
• The number in front "fine tunes" the power of ten.

ANSWERS:

14) 5.213 x 10³

15) 7.32 x 10⁴

16) 2.321 x 10¹

17) 2.1 x 10¹⁰

18) 4.713 x 10⁹

19) 2 x 10^-2

20) 3.14 x 10^-4

21) 4.3791 x 10^-10

22) 2,000

23) 233,100

24) 95,100,000,000,000,000,000,000

25) 0.005

26) 0.000076278

27) 1,000 +100,000 = 101,000

28) 251 + 52,300 = 52,551

29) 10,000 - 100 = 9,900

30) 20,000 - 700 =19,300

31) 10⁽¹²⁺⁵⁾ = 10¹⁷ = 100,000,000,000,000,000

32) (7.2 x 2.12) x 10^(5-2) = 15.264 x 10³ = 15,264

33) 10^(9-4) = 10⁵ = 100,000

34) (2.3 / 9.2) x 10^(7-2) = (0.25) x 10⁵ = 25,000