**Unformatted text preview: **1106 APPENDIX A Mathematical Operations - SAMPLE EXERCISE 1 l Using Exponential Notation
Perform each of the following operations, using your calculator where possible: (a) Write the number 0.0054 in standard exponential notation
(b) (5.0 x 104) + (4.7 X 10*)
(c) (5.98 x 1012x277 X 105) (d) \/4 1.75 x 10’12 SOLUTION (a) Because we move the decimal point three places to the right to convert 0.0054 to
5.4, the exponent is —3: 5.4 x 10'3 Scientiﬁc calculators are generally able to convert numbers to exponential notation
using one or two keystrokes Consult your instruction manual to see how this opera—
tion is accomplished on your calculator. (b) To add these numbers longhand, we must convert them to the same exponent. (5.0 x 10’2) + (0.47 x 10’2) = (5.0 + 0.47) x 10’2 = 5.5 X 10’2 (Note that the result has only two signiﬁcant ﬁgures.) To perform this operation on a
calculator, we enter the first number, strike the + key, then enter the second number
and strike the = key. (c) Performing this operation longhand, we have (5.98 x 2.77) x 1012’5 = 16.6 X 107 = 1.66 X 108 On a scientific calculator, we enter 5.98 X 1012, press the X key, enter 2.77 X 10‘5,
and press the = key. (d) To perform this operation on a calculator, we enter the number, press the W key
(or the INV and yI keys), enter 4, and press the = key. The result is 1.15 X 10‘3. - PRACTICE EXERCISE
Perform the following operations: (a) Write 67,000 in exponential notation, showing two signiﬁcant figures
(b) (3378 X 10’3) — (4.97 x 105) (c) (1.84 X 1015x745 X 102) (d) (6.67 x 10'8)3 Answers: (a) 6.7 X 104, (b) 3328 X 1073, (c) 2.47 X 1016, (d) 2.97 x 10’22 A.2 LOGARITHMS Common Logarithms The common, or base-10, logarithm (abbreviated log) of any number is the
power to which 10 must be raised to equal the number. For example, the com-
mon logarithm of 1000 (written log 1000) is 3 because raising 10 to the third
power gives 1000. 103 = 1000, therefore, log 1000 = 3 Further examples are log 105 = 5
log 1 = 0 (Remember that 100 = 1)
log 10‘2 = —2 In these examples the common logarithm can be obtained by inspection. How-
ever, it is not possible to obtain the logarithm of a number such as 31.25 by in-
spection. The logarithm of 31.25 is the number x that satisﬁes the following
relationship: 10" = 31.25 ...

View
Full Document