directions: on a separate sheet of paper, write your name, period, and answers. solve the below problems without a calculator and use this paper as scratch paper. 12. multiply the below numbers by 2

a. 42                              b. 17                  c. 36

d. 45                              e. 16                    f. 24

g. 32                                h. 48

13. divide the below numbers by 2

a. 44                         e. 46

b. 98                          f. 78

c. 86                          g. 56

d. 38

Calculations involving powers of ten

14. multiplication

a. 10 5 * 10 7 =

b. (5.0 * 10 4 ) * (3.0 * 10 23 ) =

c. 10 8 * 10 -5 =

d. 10 7 * 10 -15 =

e. (7.0 * 10 14 ) * (3.0 * 10 -23 ) =

15. division

a. 10 5 ÷ 10 7 =

b. (35.0 * 10 4 ) ÷ (7.0 * 10 23 ) =

c. 10 8 ÷ 10 -5 =

d. 10 7 ÷ 10 -15 =

e. (24.0 * 10 14 ) ÷ (3.0 * 10 -23 ) =

16. multiplication & division 17. logarithm (base 10 system)

review:

log (a * b) = log a + log b

ex1. log (5 * 10 4) = log (5) + log (10 4) = log 5 + 4 ≈4.__.

ex2. log (5 * 10 - 4) = log (5) + log (10 - 4) = log 5 - 4 ≈3.__.

as any number can be expressed using scientific notation, you should be able to use the above property to estimate the log of any number. to get a better estimate, memorize

log 1 = 0           log 6 ≈ 0.8

log 2 ≈ 0.3       log 7 ≈ 0.8

log 3 ≈ 0.5       log 8 ≈ 0.9

log 4 ≈ 0.6       log 9 ≈ 1

log 5 ≈ 0.7       log 10 = 1

a. log (10 9) =

b. log (10 -12) =

c. log (5 * 10 9) ≈

d. log (8 * 10 -12) ≈

e. log (7 * 10 -5) ≈

f. log (3 * 105) ≈

source: problems 1 - 13: page 13; http://www.chemreview.net/WeekOneFiles.pdf