Full file at Scientific Measurements

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1 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) cm and (d) cm each have an uncertainty of ± 0.05 cm. 6. (c) g is the only mass with an uncertainty of ± g. 8. (d) 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) g 4 significant digits 12. Measurement Significant Digits (a) 0.5 s 1 significant digit 0.50 s 2 significant digits (c) s 3 significant digits (d) 500 s 1 significant digit 14. Measurement Significant Digits (a) g 2 significant digits

2 g 3 significant digits (c) g 3 significant digits (d) g 1 significant digit Section 2.3 Rounding Off Nonsignificant Digits 16. Example Rounded Off (a) (c) (d) Example Rounded Off (a) (c) (d) Section 2.4 Adding and Subtracting Measurements 20. (a) 0.55 cm cm cm = cm rounds to 54.0 cm 4.0 cm cm cm = cm rounds to 21.3 cm 22. (a) cm 10.5 cm = 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 = cm 3 rounds to 3 cm cm 2.55 cm 1.1 cm = cm 3 rounds to 14 cm 3 (c) 12.0 cm cm = 12.0 cm 3 rounds to 12.0 cm 3 (d) 22.1 cm cm = cm 3 rounds to 17 cm (a) (c) 66.3 g 7.5 ml = 8.84 g/ml rounds to 8.8 g/ml 12.5 g 4.1 ml = g/ml rounds to 3.0 g/ml g 10.0 ml = g/ml rounds to 4.26 g/ml

3 (d) g ml = g/ml rounds to g/ml Section 2.6 Exponential Numbers 28. (a) = = ( 1 3 )4 = (a) = = ( 1 10 )4 = Number Scientific Notation (a) ,000,000,000, Number Scientific Notation (a) 100,000,000,000,000, Scientific Notation Number (a) Section 2.7 Scientific Notation 38. Number Scientific Notation (a) 1,010,000,000,000, (c) 94,500,000,000,000, (d) radon atoms g/lead atom

4 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 inches 2.54 centimeters 1 inches = centimeters

5 milligrams 15.4 grains 1000 milligrams = 5.01 grains teaspoons 1 tablespoon 3 teaspoons = 5.0 tablespoons weeks 7 days 1 week = 84.0 days troy ounces 31.1 grams 1 troy ounce = 1560 grams year 365 days 1 year 24 hours 1 day 60 minutes 1 hour 60 seconds 1 minute cm 1 second = cm Section 2.10 The Percent Concept ml oxygen 100 ml air 20.9 ml oxygen = 1080 ml air gal 12.5 gal 100% = 12.0% of gasohol is ethanol g table salt 39.3 g sodium 100 g table salt = g sodium kg total 54.3 kg Titania 100 kg total = kg Titania

6 76. Total quantity = g copper and zinc Quantity of zinc = g Quantity of copper = g g = g Percent of copper: g g 100% = 2.5% copper General Exercises ml (±1 ml) 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) Mass of a neutron = g Mass of a proton = g Mass difference: ( g) ( g) = g 88. Total distance = distance from the Earth to the Moon + distance from the Moon to Mars Total distance: miles miles = miles

7 billion years = years years 365 days 1 year 24 hours 1 day 60 minutes 1 hour = minutes 92. AB : 276 patients patients 100% = 0.498% AB type troy pound 12 troy ounces 1 troy pound 31.1 grams 1 troy ounce = 373 grams (gold)