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Chapter 1 Matter, Measurement, and Problem Solving 9 (d) 5.99 -5.572 0.418 = 0.42 Round the intermediate answer to two decimal places to reflect the quantity with the fewest decimal places (5.99). Round the last digit up because the first nonsignificant digit is 8. 1.87 Perform operations in parentheses first. Keep track of significant figures in each step by noting the last significant digit in an intermediate result. (a) (24.6681 X 2.38) + 332.58 = 58.710078 +332.58 391.290078 = 391.3 The first intermediate answer has one significant digit to the right of the decimal because it is allowed three significant figures [reflecting the quantity with the fewest significant figures (2.38)]. Underline the most signifi- cant digit in this answer. Round the next intermediate answer to one decimal place to reflect the quantity with the fewest decimal places (58.7). Round the last digit up because the first nonsignificant digit is 9. (85.3 21.489) 63.811 (b) 0.0059 = 0.0059 = 1.081542 X 10⁴ = 1.1 X 10⁴ The first intermediate answer has one significant digit to the right of the decimal to reflect the quantity with the fewest decimal places (85.3). Underline the most significant digit in this answer. Round the next intermediate answer to two significant figures to reflect the quantity with the fewest significant figures (0.0059). Round the last digit up because the first nonsignificant digit is 8. (c) (512 ÷ 986.7) + 5.44 = 0.5189014 +5.44 5.9589014 = 5.96 The first intermediate answer has three significant figures and three significant digits to the right of the decimal, reflecting the quantity with the fewest significant figures (512). Underline the most significant digit in this answer. Round the next intermediate answer to two decimal places to reflect the quantity with the fewest decimal places (5.44). Round the last digit up because the first nonsignificant digit is 8. (d) 10⁵) ÷ 48.533 + 144.99 = 59135.02 +144.99 59280.01 = 59300 = 5.93 X 10⁴ The first intermediate answer has three significant figures, reflecting the quantity with the fewest significant figures (28.7 X Underline the most significant digit in this answer. Because the number is so large, when the addition is performed, the most significant digit is the hundreds place. Round the next intermediate answer to the hundreds place and put in scientific notation to remove any ambiguity. Note that the last digit is rounded up because the first nonsignificant digit is 8. 1.89 Given: 11.7 mL liquid; empty flask weight = 124.1 g; flask with liquid weight = 132.8 g Find: d in g/mL Conceptual Plan: Empty flask weight, flask with liquid weight liquid weight then weight, volume d (flask with liquid (flask weight) = liquid weight d = mass/volume = m/V Solution: liquid weight = (flask with liquid weight) (flask weight) = 132.8 g 124.1 g = 8.7 g liquid; then density (d) = volume mass = m V = 11.7mL 8.7g = 0.74358974g/ml = 0.74g/mL Check: The units (g/mL) are correct. The magnitude of the answer (0.74) makes physical sense because the volume is greater than the mass. Unit Conversions 1.91 (a) Given: 27.8 L Find: cm³ Conceptual Plan: L cm³ Solution: 27.8 X 1000 cm³ = 2.78 X 10⁴ cm³ Copyright © 2017 Pearson Education, Inc.