Page 26 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 1] USEFUL MATH 11

When a calculation has several steps, it is a good idea to keep an extra digit in the intermediate steps and
wait until the end to round off the final result to the correct number of significant figures. As an example,

7.9 1.8
+ = 2.44 + 5.14 = 7.58 = 7.6
3.24 0.35
If the intermediate results had been rounded off to two digits, however, the result would have been the following,
which is incorrect:
7.9 1.8
+ = 2.4 + 5.1 = 7.5 (incorrect)
3.24 0.35
For simplicity in the text and clarity in the illustrations, in this book zeros after the decimal point have usually
been omitted from values given in the problems. It should be assumed that, for example, when a resistance of
5 is quoted, what is really meant is 5.00 .

Multiple-Choice Questions

1.1. In which of the following equations is x not equal to 2?
√
2
2
2
(a) x + 4x = 12 (c) 6x + 25 = 7(5 − x )
√
2
2
3
(b) 2x + 5x = 14 (d) (x + 6) = 50x
−4
3
−4
1.2. The value of (5.0 × 10 )(6.0 × 10 )/(1.5 × 10 ) is
(a)2.0 × 10 −11 (c)2.0 × 10 −10
(b)9.5 × 10 −11 (d)2.0 × 10 −4
−6 2
1.3. The value of 1/(2.0 × 10 ) is
(a)2.5 × 10 5 (c)5.0 × 10 11
(b)2.5 × 10 11 (d)2.5 × 10 12
1.4. The prefix kilo- represents
(a)10 (c) 1000
(b) 100 (d) 1,000,000
1.5. A millimeter is
(a) 0.001 m (c) 0.1 m
(b) 0.01 m (d)10 m

1.6. The longest of the following is
(a) 1 mm (c) 0.01 in.
(b) 0.00001 km (d) 0.001 ft
1.7. The shortest of the following is
3
4
(a)10 in. (c)10 ft
4
(b)10 m (d) 0.1 mi
1.8. A person is 180 cm tall. This is equivalent to approximately
(a) 4 ft 6 in. (c) 5 ft 11 in.
(b) 5 ft 9 in. (d) 7 ft 1 in.