Problems B
61
by measuring the height to which water rises at 25.0°C. Several attempts yield
the following heights: 75.7 mm; 75.6 mm; 75.3 mm; 75.8 mm; 75.2 mm. Find
the average deviation of these heights and the 80% confidence interval for the
mean, expressing both in parts per thousand.
10. At 25.00°C, the density and surface tension of water are 0.997044 g/ml and
71.97 dynes/cm, respectively. What actual values for these properties should
be used with the data of Problem 9 to determine the radius of the capillary?
11. A sample of a copper alloy is to be analyzed for copper by first dissolving the
sample in acid and then plating out the copper electrolytically. The weight of
copper plated is to be measured on a balance that is sensitive to 0.1 mg. The
alloy is approximately 5% copper. What size of sample should be taken for
analysis so that the error in determining the weight of copper plated out does
not exceed one part per thousand? (Remember that two weighings are needed
in order to find the weight of copper.)
PROBLEMS B
12. State the number of significant figures in each of the following measurements,
(a) 6822; (b) 6.822 x 10-<; (c) 6.82; (d) 682; (e) 0.006820; (f) 6.82 x 10
6
; (g)
0.0682; (h) 34 thousandths; (i) 167 million; (j) 62 hundredths.
13. Express the answer in each of the following calculations to the proper number
of significant figures (assume that the numbers represent measurements).
(a) 0.0657 + 23.77 + 5.369 + 0.0052
(b) 365.72 - 0.583
(c) 365.2 + 27.3 + 968.45 + 5.62
(d) 4.27 x 10-' + 1.05 x 10~« + 5 x \0~
K + 1.234 x 10-'
, , 65.4 x 1.23 x 464
(g)
(h)
6.55 x 1Q-" x 2.045 x 7.34 x 10
r
'
565 x 432
5280 x (2885)
:! x 6.570 x 1Q-'4.6295 x 0.8888
96.08 x 4.712 x 10-- x 7.308 x 1Q6.547 x 10-7 x 6.022 x 10
2:i
14. Water analysts often report trace impurities in water as "parts per million"—
that is, parts by weight of impurity per million parts by weight of water. A
swimming pool whose dimensions are-20 x 50 x 9 m has 14 Ib of chlorine added
as a disinfectant. How many parts per million of chlorine are present in this
swimming pool? (Assume that the density of water is 1.00 g/ml.)
15. State the precision, in both percentage and parts per thousand, with which
each of the following measurements is made.
(a) 6822 with a standard deviation of 4.0
(b) 6.822 x 10-' with a standard deviation of 0.00040
61
by measuring the height to which water rises at 25.0°C. Several attempts yield
the following heights: 75.7 mm; 75.6 mm; 75.3 mm; 75.8 mm; 75.2 mm. Find
the average deviation of these heights and the 80% confidence interval for the
mean, expressing both in parts per thousand.
10. At 25.00°C, the density and surface tension of water are 0.997044 g/ml and
71.97 dynes/cm, respectively. What actual values for these properties should
be used with the data of Problem 9 to determine the radius of the capillary?
11. A sample of a copper alloy is to be analyzed for copper by first dissolving the
sample in acid and then plating out the copper electrolytically. The weight of
copper plated is to be measured on a balance that is sensitive to 0.1 mg. The
alloy is approximately 5% copper. What size of sample should be taken for
analysis so that the error in determining the weight of copper plated out does
not exceed one part per thousand? (Remember that two weighings are needed
in order to find the weight of copper.)
PROBLEMS B
12. State the number of significant figures in each of the following measurements,
(a) 6822; (b) 6.822 x 10-<; (c) 6.82; (d) 682; (e) 0.006820; (f) 6.82 x 10
6
; (g)
0.0682; (h) 34 thousandths; (i) 167 million; (j) 62 hundredths.
13. Express the answer in each of the following calculations to the proper number
of significant figures (assume that the numbers represent measurements).
(a) 0.0657 + 23.77 + 5.369 + 0.0052
(b) 365.72 - 0.583
(c) 365.2 + 27.3 + 968.45 + 5.62
(d) 4.27 x 10-' + 1.05 x 10~« + 5 x \0~
K + 1.234 x 10-'
, , 65.4 x 1.23 x 464
(g)
(h)
6.55 x 1Q-" x 2.045 x 7.34 x 10
r
'
565 x 432
5280 x (2885)
:! x 6.570 x 1Q-'4.6295 x 0.8888
96.08 x 4.712 x 10-- x 7.308 x 1Q6.547 x 10-7 x 6.022 x 10
2:i
14. Water analysts often report trace impurities in water as "parts per million"—
that is, parts by weight of impurity per million parts by weight of water. A
swimming pool whose dimensions are-20 x 50 x 9 m has 14 Ib of chlorine added
as a disinfectant. How many parts per million of chlorine are present in this
swimming pool? (Assume that the density of water is 1.00 g/ml.)
15. State the precision, in both percentage and parts per thousand, with which
each of the following measurements is made.
(a) 6822 with a standard deviation of 4.0
(b) 6.822 x 10-' with a standard deviation of 0.00040