Page 39 - Theory and Problems of BEGINNING CHEMISTRY

28 MATHEMATICAL METHODS IN CHEMISTRY [CHAP. 2

2.29. Make the following conversions:

3
2
(a) Change 6.3 cm to m 2 (e) Change 1.7 m to kL
2
3
(b) Change 13 cm to m 3 (f ) Change 3.3 m to cm 2
(c) Change 9.2 L to cm 3 (g) Change 219 mL to cm 3
3
(d) Change 9.6 dm to L
2
1m 1kL
Ans. (a)6.3cm 2 = 0.000 63 m 2 (e)1.7m 3 = 1.7kL
100 cm 1m 3
2
3
100 cm
1m 2 2
(b)13 cm 3 = 0.000 013 m 3 (f) 3.3m = 33 000 cm
100 cm 1m
1000 cm 3
3 1cm 3
(c)9.2L = 9200 cm 3 (g) 219 mL = 219 cm
1L 1mL

1L
(d)9.6dm 3 = 9.6L
1dm 3
2.30. Give the volume corresponding to each of the following in terms of a dimension involving length cubed:
(a) 1 kL, (b)2L,(c) 3 mL, and (d)4 µL.
Ans. (a)1 m 3 (b)2dm 3 (c)3cm 3 (d)4mm 3
EXPONENTIAL NUMBERS
3
2.31. In the number 5.0×10 , identify (a) the coefficient, (b) the exponent, (c) the base, and (d) the exponential
part.
Ans. (a) 5.0 (b)3 (c)10 (d)10 3
2.32. What is the meaning of each of the following: (a) ten squared, (b) ten cubed, (c) ten to the fourth power?

Ans. (a)10 2 (b)10 3 (c)10 4
2.33. Which of the following numbers are in standard exponential form?

(a)11.0 × 10 −3 (f) 0.12 × 10 5
(b)6.7 × 10 0 (g)0.1 × 10 5
(c)3 × 10 7 (h)4.4 × 10 3
(d)0.77 × 10 7 (i) 1.0 × 10 4
(e)1.23 × 10 −4

Ans. (b), (c), (e), (h), and (i)
6
3 2
2.34. Show by writing out the explicit meaning of the exponential parts that (3.0 × 10 ) = 9.0 × 10 .
3 2
3
3
Ans. (3.0 × 10 ) = (3.0 × 10 )(3.0 × 10 )
= 3.0 × 3.0 × (10 × 10 × 10) × (10 × 10 × 10)
= 9.0 × 10 6
2.35. Simplify:
1 1 10 −4
(a) (b) (c)
10 −3 10 6 10 −4

0
Ans. (a)10 3 (b)10 −6 (c)10 = 1