Page 314 - Theory and Problems of BEGINNING CHEMISTRY

APP.] SCIENTIFIC CALCULATIONS 303

Ans. (a) 2 . 2 2 ÷ 1 . 0 3 = log (b) 2 . 2 2 ÷ 1 . 0 3 log =

x = 0.334 x = 173
Note the similarity of the keystroke sequences but the great difference in answers.

Significant Figures
An electronic calculator gives its answers with as many digits as are available on the display unless the last
digits are zeros to the right of the decimal point. The calculator has no regard for the rules of significant figures
(Sec. 2.5). You must apply the rules when reporting the answer. For example, the reciprocal of 9.00 is really
0.111, but the calculator displays something like 0.111 111 11. Similarly, dividing 8.08 by 2.02 should yield 4.00,
but the calculator displays 4. You must report only the three significant 1s in the first example and must add the
two significant 0s in the second example.

Summary
Note especially the following points that are important for your success:
1. Variables, constants, and units are represented with standard symbols in scientific mathematics (for example,
d for density). Be sure to learn and use the standard symbols.
2. Units may be treated as algebraic quantities in calculations.
3. Be sure to distinguish between similar symbols for variables and units. Variables are often printed in italics.
For example, mass is symbolized by m, and meter is represented by m. Capitalization can be crucial: v
represents velocity and V stands for volume.
4. Algebraic and calculator operations must be done in the proper order (according to the rules of precedence).
(See Table A-1.) Note that multiplication and division are treated somewhat differently on the calculator
than in algebra.
5. Operations of equal precedence are done left to right except for exponentiation and unary minus, which are
done right to left.

Solved Problems
SCIENTIFIC ALGEBRA
A.1. Simplify each of the following:

27y 1 x
(a)3x = 42 (b) (c) = 6.00 (d ) 14 (e) 23(x − 16) = 0
3x x 42
(f )(x + 9) − (2x + 1)
Ans. Be sure to distinguish between equations and expressions when simplifying.
(a) x = 14 (b)9y/x (c) x = 0.167 (d)0.33x (e) x = 16 ( f ) −x + 8

A.2. Using your calculator, find the value of x from
x = (a + b) − (c + d)
where a =−3, b = 5, c =−6, and d = 10. Repeat this calculation twice, once using the parentheses
keys and once without using them.
Ans. x =−2

A.3. Simplify each of the following, if possible:
V 1 T 2 P 1 V 1 P 2 2P 2
(a) (b) (c) =
V 1 T 2 P 2 V 2 3T 1 T 2