Page 41 - Theory and Problems of BEGINNING CHEMISTRY

30 MATHEMATICAL METHODS IN CHEMISTRY [CHAP. 2

2
2
2.41. (a) Change 2.67 mi to square feet. (b) Change 2.67 km to square meters.
2 2
5280 ft 1000 m
7
6
Ans. (a)2.67 mi 2 = 7.44 × 10 ft 2 (b)2.67 km 2 = 2.67 × 10 m 2
1mi 1km
3
5
2.42. Calculate the number of cubic meters in 6.4 × 10 mm .
3
1m

5
Ans. 6.4 × 10 mm 3 = 6.4 × 10 −4 m 3
1000 mm
3
2.43. Which is bigger, 4.0 L or 4000 mm ?
3
3
Ans. 4.0 L is bigger. It is equal to 4000 cm or 4 000 000 mm .
3
2.44. Change 7.3 g/cm to kilograms per cubic meter.

7.3g 100 cm 3 1kg
3
Ans. = 7.3 × 10 kg/m 3
cm 3 1m 1000 g
3
3
3
3
2.45. Given that 1 L = 1dm , calculate the number of liters in (a)1m ,(b)1cm , and (c)1mm .
10 dm 1L 1dm 1L
3 3
Ans. (a)1 m 3 = 1000 L (c)1 mm 3 = 1 × 10 −6 L
1m 1dm 3 100 mm 1dm 3
1dm 1L
3
(b)1 cm 3 = 0.001 L
10 cm 1dm 3
SIGNIFICANT DIGITS
2.46. What is the difference between the number of significant digits and the number of decimal places in a
measurement?
Ans. The number of significant digits is the number of digits that reflect the precision of the measurement. The
number of decimal places is the number of digits after the decimal point. The two have little to do with each
other, so do not get them confused.
2.47. Underline the significant digits in each of the following measurements. If a digit is uncertain, place a
question mark below it.
3
(a) 2.03 m, (b) 47.0 m, (c) 51.05 m, (d)9.00 × 10 m, (e) 6.100 m, ( f ) 0.0400 m, (g) 1.110 m,
(h) 30.0 m, (i) 400 m
Ans. (a) 2.03 m rule 2 (f) 0.0400 m rules 1 and 3
(b) 47.0 m rule 3 (g) 1.110 m rule 3
(c) 51.05 m rule 2 (h) 30.0 m rules 2 and 3
3
(d) 9.00 × 10 m rule 3 (i) 400 rule 4
??
(e) 6.100 m rule 3
2.48. To the correct number of significant digits, calculate the number of
(a) millimeters in 4.00 m (c) millimeters in 13.57 cm
(b) kilograms in 49 g (d) centimeters in 0.0040 m

3
Ans. (a)4.00 × 10 mm (three significant digits) (c) 135.7 mm (four significant digits)
(b) 0.049 kg (two significant digits) (d) 0.40 cm (two significant digits)