CHAPTER Scientific Measurements 2 Section 2.1 Uncertainty in Measurements 2. Unit Quantity Unit Quantity (a) meter length gram mass (c) liter volume (d) second time 4. (c) 15.50 cm and (d) 20.05 cm each have an uncertainty of ± 0.05 cm. 6. (c) 75.518 g is the only mass with an uncertainty of ± 0.001 g. 8. (d) 25.50 ml is the only reading with an uncertainty of ± 0.05 ml. Section 2.2 Significant Digits 10. Measurement Significant Digits (a) 0.05 g 1 significant digit 0.10 g 2 significant digits (c) 25.0 g 3 significant digits (d) 10.10 g 4 significant digits 12. Measurement Significant Digits (a) 0.5 s 1 significant digit 0.50 s 2 significant digits (c) 0.500 s 3 significant digits (d) 500 s 1 significant digit 14. Measurement Significant Digits (a) 1.2 10 0 g 2 significant digits
4.50 10 1 g 3 significant digits (c) 5.02 10 1 g 3 significant digits (d) 1 10 2 g 1 significant digit Section 2.3 Rounding Off Nonsignificant Digits 16. Example Rounded Off (a) 20.155 20.2 0.204 500 0.205 (c) 2055 2060 (d) 0.2065 0.207 18. Example Rounded Off (a) 4.123 10 5 4.12 10 5 4.456 10 10 4.46 10 10 (c) 4.000 10 7 4.00 10 7 (d) 4.075 10 12 4.08 10 12 Section 2.4 Adding and Subtracting Measurements 20. (a) 0.55 cm + 36.15 cm +17.3 cm = 54.00 cm rounds to 54.0 cm 4.0 cm + 16.3 cm + 0.95 cm = 21.25 cm rounds to 21.3 cm 22. (a) 22.10 cm 10.5 cm = 11.60 cm rounds to 11.6 cm 10.0 cm 0.15 cm = 9.85 cm rounds to 9.9 cm Section 2.5 Multiplying and Dividing Measurements 24. (a) 5.1 cm 1.25 cm 0.5 cm = 3.1875 cm 3 rounds to 3 cm 3 5.15 cm 2.55 cm 1.1 cm = 14.44575 cm 3 rounds to 14 cm 3 (c) 12.0 cm 2 1.00 cm = 12.0 cm 3 rounds to 12.0 cm 3 (d) 22.1 cm 2 0.75 cm = 16.575 cm 3 rounds to 17 cm 3 26. (a) (c) 66.3 g 7.5 ml = 8.84 g/ml rounds to 8.8 g/ml 12.5 g 4.1 ml = 3.04878 g/ml rounds to 3.0 g/ml 42.620 g 10.0 ml = 4.262 g/ml rounds to 4.26 g/ml
(d) 91.235 g 10.00 ml = 9.1235 g/ml rounds to 9.124 g/ml Section 2.6 Exponential Numbers 28. (a) 3 3 3 3 = 3 4 1 3 1 3 1 3 1 3 = ( 1 3 )4 = 3 4 30. (a) 10 10 10 10 10 10 = 10 6 1 10 1 10 1 10 1 10 = ( 1 10 )4 = 10 4 32. Number Scientific Notation (a) 1 10 12 1,000,000,000,000 1 10 22 0.000 000 000 000 000 000 000 1 34. Number Scientific Notation (a) 100,000,000,000,000,000 1 10 17 0.000 000 000 000 001 1 10 15 36. Scientific Notation Number (a) 1 10 0 1 1 10 10 0.000 000 000 1 Section 2.7 Scientific Notation 38. Number Scientific Notation (a) 1,010,000,000,000,000 1.01 10 15 0.000 000 000 000 456 4.56 10 13 (c) 94,500,000,000,000,000 9.45 10 16 (d) 0.000 000 000 000 000 019 50 1.950 10 17 40. 2.69 10 23 radon atoms 42. 3.44 10 22 g/lead atom
Section 2.8 Unit Equations and Unit Factors 44. Unit Equation (a) 1 quart = 2 pints 1 century = 100 years 46. Unit Factors 1 quart (a) 2 pints and 2 pints 1 quart 1 century 100 years and 100 years 1 century 48. (a) 1 kilogram = 1000 grams is an exact equivalent. 1 kilogram = 2.20 pounds is an approximate equivalent because it relates two different systems of measurement (English and metric). 50. (a) 1 month = 4 weeks is an approximate equivalent because the number of days in a month varies. 1 hour = 60 minutes is an exact equivalent. 52. (a) 1 kilogram = 1000 grams has an infinite number of significant digits because it is an exact equivalent. 1 kilogram = 2.20 pounds has three significant digits because it is an approximate equivalent. 54. (a) 1 month = 4 weeks has only one significant digit because it is an approximate equivalent. 1 hour = 60 minutes has an infinite number of significant digits because it is an exact equivalent. Section 2.9 Unit Analysis Problem Solving 56. 12 inches 2.54 centimeters 1 inches = 3.0 10 2 centimeters
58. 325 milligrams 15.4 grains 1000 milligrams = 5.01 grains 60. 15 teaspoons 1 tablespoon 3 teaspoons = 5.0 tablespoons 62. 12.0 weeks 7 days 1 week = 84.0 days 64. 50.0 troy ounces 31.1 grams 1 troy ounce = 1560 grams 66. 1.00 year 365 days 1 year 24 hours 1 day 60 minutes 1 hour 60 seconds 1 minute 3.00 1010 cm 1 second = 9.46 10 17 cm Section 2.10 The Percent Concept 68. 225 ml oxygen 100 ml air 20.9 ml oxygen = 1080 ml air 70. 1.50 gal 12.5 gal 100% = 12.0% of gasohol is ethanol 72. 0.375 g table salt 39.3 g sodium 100 g table salt = 0.147 g sodium 74. 3.87 10 21 kg total 54.3 kg Titania 100 kg total = 2.10 10 21 kg Titania
76. Total quantity = 2.554 g copper and zinc Quantity of zinc = 2.490 g Quantity of copper = 2.554 g 2.490 g = 0.064 g Percent of copper: 0.064 g 2.554 g 100% = 2.5% copper General Exercises 78. 1.000 10 3 ml (±1 ml) 80. 3.00 10 8 meters per second The velocity must be expressed in scientific notation because the rounded value, 300,000,000 meters per second, has only one significant digit. 82. Remaining length: 255 cm 2(25.0 cm) = 205 cm 84. Exponential Number Scientific Notation (a) 0.170 10 2 1.70 10 1 0.00350 10 1 3.50 10 4 86. Mass of a neutron = 1.6749 10 24 g Mass of a proton = 1.6726 10 24 g Mass difference: (1.6749 10 24 g) (1.6726 10 24 g) = 2.3 10 27 g 88. Total distance = distance from the Earth to the Moon + distance from the Moon to Mars Total distance: 2.39 10 5 miles + 4.84 10 7 miles = 4.86 10 7 miles
90. 4.1 billion years = 4.1 10 9 years 4.1 10 9 years 365 days 1 year 24 hours 1 day 60 minutes 1 hour = 2.2 10 15 minutes 92. AB : 276 patients 55 368 patients 100% = 0.498% AB type 94. 1 troy pound 12 troy ounces 1 troy pound 31.1 grams 1 troy ounce = 373 grams (gold)