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.

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

1) 10^{4} =

2) 10^{7} =

3) 10^{17} =

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) 10^{1}

8) 10^{5}

9) 10^{18}

10) 10^{-3}

11) 10^{0}

12) 10^{-9}

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

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 10^{3 }=

23) 2.331 x 10^{5 }=

24) 9.51 x 10^{22} =

25) 5 x 10^{-3 }=

26) 7.6278 x 10^{-5} =

27) 10^{3} + 10^{5} =

28) (2.51 x 10^{2} ) + (5.23 x 10^{4} ) =

29) 10^{4} - 10^{2} =

30) (2 x 10^{4} ) - (7 x 10^{2} ) =

31) 10^{12} x 10^{5} =

32) (7.2 x 10^{5} ) x (2.12 x 10^{-2} ) =

33) 10^{9} / 10^{4} =

34) (2.3 x 10^{7}) / (9.2 x 10^{2}) =

** 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,
10
^{3}, 10^{8}, or 10^{-5}). - The number in front "fine tunes" the power of ten.

**ANSWERS:**

14) 5.213 x 10^{3}

15) 7.32 x 10^{4}

16) 2.321 x 10^{1}

17) 2.1 x 10^{10}

18) 4.713 x 10^{9}

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)} = 10^{17}
= 100,000,000,000,000,000

32) (7.2 x 2.12) x 10^{(5-2)} =
15.264 x 10^{3} = 15,264

33) 10^{(9-4)} = 10^{5} =
100,000

34) (2.3 / 9.2) x 10^{(7-2)} =
(0.25) x 10^{5} = 25,000

Layden -17jan00