Page 42 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 2] MATHEMATICAL METHODS IN CHEMISTRY 31

2.49. In which of the following problems are the numbers of significant digits retained?

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(a) (65.4cm )/(60.5cm) (c) (65.4cm )(60.5cm)
(b) (65.4cm) + (60.5cm) (d) (65.4cm) − (60.5cm)
Ans. (a) and (c). [In (b) the number increases to 4, in (d) it decreases to 2.]
2.50. Calculate the answer to each of the following expressions to the correct number of significant digits:

(a)6.06 cm × 1.8cm (e)29.0cm + 0.004 cm
(b)6.06 cm − 1.8cm (f)9.44 cm + 4.66 cm − 0.02 cm
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(c) (6.06 g)/(1.8cm ) (g)4.77 cm + 1.506 cm
(d)1.234 cm + 5.6cm − 0.078 cm

Ans. (a)11 cm 2 (c) 3.4 g/cm 3 (e) 29.0 cm (g) 6.28 cm
(b) 4.3 cm (d) 6.8 cm (f ) 14.08 cm

2.51. Calculate the answer to each of the following expressions to the correct number of significant digits:

(a) (1.66 cm + 7.3cm) × 4.00 cm (e)1.11 × 10 cm × 3.17 cm × 1.00 × 10 cm
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(b)2.29 cm × (1.7cm − 4.213 cm) (f) 5.7 × 10 −3 cm − 7.8 × 10 −3 cm
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(c) (1.91 cm × 4.8cm) − 5.71 cm 2 (g) (2.170 cm × 7.11 cm)+(5.820 cm −7.16 cm )
(d) 7130 cm − 2.13 cm
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Ans. (a)36cm (The sum has only two significant digits.) (b) −5.7cm 2 (c)3.5cm 2 (d) 7128 cm
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(e)3.52 × 10 cm 3 (f ) −2.1 × 10 −3 cm (g)14.1cm 2
2.52. Perform the following calculations to the proper number of significant digits. All measurements are in
centimeters.
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(a)1.20 × 10 − 9.8 × 10 6 (d)6.66 × 10 − 6.02 × 10 6
(b)6.66 × 10 −3 − 4.78 × 10 −2 (e)2.6 × 10 −19 − 1.2 × 10 −17
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(c)7.7 × 10 − 3.7 × 10 8
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Ans. (a)1.10 × 10 cm (d)6.06 × 10 cm
(b) −4.11 × 10 −2 cm (e) −1.2 × 10 −17 cm
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(c) 7.3 × 10 cm
2.53. Calculate each answer to the correct number of significant digits: (a) (3.69 g)/(1.23 mL),
(b) (369 g)/(1.23 L), and (c) (987 g)/(1.5 L).
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Ans. (a) 3.00 g/mL (b)3.00 × 10 g/L (c) 660 g/L = 0.66 kg/L.
Three significant digits are required in (a) and in (b); two significant digits are required in (c).
2.54. Explain why every zero in the coefficient is significant in a number properly expressed in standard
exponential notation.
Ans. No zeros are needed for the sole purpose of determining the magnitude of the number. (The exponential part
of the number does that.) The only other reason a zero would be present is if it were significant.

2.55. To how many decimal places should you report the reading of (a) a 50-mL buret (graduated in 0.1 mL)
and (b) an analytic balance (calibrated to 0.001 g)?
Ans. (a)2 (b)4
(One estimated digit in each.)