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1 Matter and Measurement Solutions to Exercises (b) Average deviation = Σ I value average /3 I. 22.52 22.51 + 22.48 22.51 + 22.54 22.51 I /3 = 0.02 II. 22.64 - 22.61 I + 22.58 22.61 + 22.62 - 22.61 /3 = 0.02 The two sets display the same precision, even though set I is more accurate. 1.61 (a) Appropriate. The number 22,727,000 implies a precision of one part per thousand, or 0.1%. This is an appropriate level of precision for the accounting records of a company like Apple Computer. (b) Appropriate. Rainfall data can be measured to a precision of at least one decimal place. Calculating annual rainfall and average annual rainfall involves addition, which dictates that significant figures are determined by the least number of decimal places in the data being summed. (c) Appropriate. The percentage has three significant figures. In a population as large as the United States, the number of people named Brown can surely be counted by census data or otherwise to a precision of three significant figures. (d) Inappropriate. Letter grades are posted at most to two decimal places and three significant figures (if plus and minus modifiers are quantified). The grade-point- average, obtained by addition and division, cannot have more decimal places or significant figures than the numbers being averaged. 1.62 (a) volume (b) area (c) volume (d) density (e) time (f) length (g) temperature m kg-m 1.63 (a) (b) (c) kg m 1 kg kg 1 kg (d) X = (e) X = m S (f) m S 1.64 (a) 2.4 10⁵ mi X 1.609 1mi km 1000 1km m = 3.862 10⁸ = 3.9 10⁸ m (b) 2.4 10⁵ mi 1.609 1 mi km 350 1hr km 60 min min = 4.0 10⁶ S (c) 3.862 10⁸ m 2 3.00 1s 10⁸ = 2.574 = (d) 29.783 S km 1.6093 km 1 min 60 1hr min = 6.6624 10⁴ mi/hr 1.65 (a) 575 ft 12 1ft in 2.54 1in cm 10 1cm mm 1 1.55 quarter mm = 1.1307 10⁵ = 1.13 10⁵ quarters 13