Page 29 - Schaum's Outline of Theory and Problems of Applied Physics

14 USEFUL MATH [CHAP. 1

(30,000)(0.0000006) (0.002)(0.00000005)
(e) (h)
(1000)(0.02) 0.000004
0.0001 (400)(0.00006)
(f) (i)
(60,000)(200) (0.2)(20,000)
(200)(0.00004) (0.06)(0.0001)
(g) (j)
400,000 (0.00003)(40,000)

1.9. Evaluate the following and express the results in powers-of-10 notation:
−8 2
9 3
(a) (4 × 10 ) (e) (3 × 10 )
11 −2
7 2
(b) (2 × 10 ) (f) (5 × 10 )
7 −2
−4 −3
(c) (2 × 10 ) (g) (3 × 10 )
−2 5
(d) (2 × 10 )
√ √ √
1.10. Evaluate the following and express the results in powers-of-10 notation. Note that 4 = 2, 40 = 6.3, 3 4 =
√ √
1.6, 3 40 = 3.4, and 3 400 = 7.4.
√ √ √
(a) 4 × 10 6 (f) 3 4 × 10 12 (k) 3 4 × 10 −7
√ √ √
(b) 4 × 10 7 (g) 3 4 × 10 13 (l) 3 4 × 10 −8
√ √ √
(c) 4 × 10 8 (h) 3 4 × 10 14 (m) 3 4 × 10 −9
√ √
(d) 4 × 10 −4 (i) 3 4 × 10 15
√ √
(e) 4 × 10 −5 (j) 3 4 × 10 −6
7
1.11. The earth is an average of 9.3 × 10 mi from the sun. How far is this in kilometers? In meters?
1.12. How many cubic feet are there in a cubic meter?
1.13. The speed limit in many European towns is 60 km/h. How many miles per hour is this?
8
1.14. The speed of light is 3.00 × 10 m/s. What is this speed in feet per second? In miles per second? In miles per hour?
1.15. A nautical mile is 6076 ft, and 1 knot (kn) is a unit of speed equal to 1 nautical mile/h. How fast is an 8-kn boat going
in miles per hour? In feet per second?

1.16. Use the proper number of significant figures to express the results of the following calculations:
(a)93.2 + 8.56 − 12 3.24 × 10 3
(d) + 2.58 × 10 2
(b) (18.5)(2.32)/0.4163 5.11 × 10 −2
√
5
3
(c) (4.6 × 10 )(8.75 × 10 ) (e) 43

Answers to Multiple-Choice Questions

1.1. (b) 1.6. (b)
1.2. (c) 1.7. (d)

1.3. (b) 1.8. (c)

1.4. (c) 1.9. (c)
1.5. (a) 1.10. (c)