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12 Chapter 1 Matter, Measurement, and Problem Solving 1.101 Given: 435 acres Find: square miles Other: 1 acre = 1 mile = 5280 ft Conceptual Plan: acres mi² 43560 1 acre Notice that for squared units, the conversion factors must be squared. Solution: 435 acres X 43560 1 acres X (5280 = 0.6796875 mi² = 0.680 Check: The units (mi²) are correct. The magnitude of the answer (0.7) makes physical sense because an acre is much smaller than a mi²; so the answer should go down several orders of magnitude. Three significant figures are allowed because of the limitation of 435 acres (three significant figures). Round the last digit up because the first nonsignificant digit is a 7. 1.103 Given: 14 lb Find: mL Other: 80 mg/0.80 mL; 15 mg/kg body Conceptual Plan: lb kg body mg mL 1 kg body 15 mg 0.80 mL 2.205 lb 1 kg body 80 mg Solution: 14 X 1 2.205 X 1 15 mg X 0.80 80 mL = 0.9523809524 mL = 0.95 mL Check: The units (mL) are correct. The magnitude of the answer (1 mL) makes physical sense because it is a reasonable amount of liquid to give to a baby. Two significant figures are allowed because of the statement in the problem. Truncate after the last significant digit because the first nonsignificant digit is a 2. Cumulative Problems 1.105 Given: solar year Find: seconds Other: 60 seconds/minute; 60 minutes/hour; 24 hours/solar day; 365.24 solar days/solar year Conceptual Plan: yr day hr min sec 365.24 day 24 hr 60 min 60 sec 1 solar yr 1 day 1 hr 1 min Solution: 1 solar yr X 365.24 1 solar day X 24 1 day hr X 60 1 min hr X 60 1 min sec = 3.1556736 X 10⁷ sec = 3.1557 X 10⁷ sec Check: The units (sec) are correct. The magnitude of the answer (10⁷) makes physical sense because each conversion factor increases the value of the answer-a second is many orders of magnitude smaller than a year. Five significant figures are allowed because all conversion factors are assumed to be exact except for the 365.24 days/solar year (five significant figures). Round the last digit up because the first nonsignificant digit is a 7. 1.107 (a) Extensive-The volume of a material depends on how much is present. (b) Intensive-The boiling point of a material is independent of how much material you have; so these values can be published in reference tables. (c) Intensive-The temperature of a material is independent of how much is present. (d) Intensive-The electrical conductivity of a material is independent of how much material you have; so these values can be published in reference tables. (e) Extensive-The energy contained in material depends on how much is present. If you double the amount of material, you double the amount of energy. 1.109 Given: 130 °X = 212 °F and 10 °X = Find: temperature where °X = °F. Conceptual Plan: Use data to derive an equation relating °X and °F. Then set °F = °X = Z and solve for z. Solution: Assume a linear relationship between the two temperatures (y = mx + b). Let y = °F and let x = °X. The slope of the line (m) is the relative change in the two temperature scales: m = = 130 212 °X °F 10 = 120 = 1.5 Copyright © 2017 Pearson Education, Inc.