Chapter 5 Assessment All exercises with blue numbers have answers in the back of this book. 5.1 Scientific Notation and Units A. Scientific Notation 1. When the number 98,145 is written in standard scientific notation, the exponent indicating the power of 10 will be. 2. When the number 4.512 1 0 3 is written in ordinary decimal notation, it is expressed as. 3. Write each of the following as an ordinary decimal number. a. 6.235 1 0 2 c. 5.001 1 0 6 b. 7.229 1 0 3 d. 8.621 1 0 4 4. For each of the following numbers, if the number is rewritten in standard scientific notation, what will be the value of the exponent (for the power of 10)? a. 0.000067 c. 1/10,000 b. 9,331,442 d. 163.1 1 0 2 5. Express each of the following numbers in standard scientific notation. a. 9,367,421 e. 6.24 1 0 2 b. 7241 f. 6319 1 0 2 c. 0.0005519 g. 0.000000007215 d. 5.408 h. 0.721 6. Express each of the following as an ordinary decimal number. a. 4.83 1 0 2 g. 9.999 1 0 3 b. 7.221 1 0 4 h. 1.016 1 0 5 c. 6.1 1 0 0 i. 1.016 1 0 5 d. 9.11 1 0 8 j. 4.11 1 0 1 e. 4.221 1 0 6 k. 9.71 1 0 4 f. 1.22 1 0 3 l. 9.71 1 0 4 7. Write each of the following numbers in standard scientific notation. a. 142.3 1 0 3 e. 0.0251 1 0 4 b. 0.0007741 1 0 9 f. 97,522 1 0 3 c. 22.7 1 0 3 g. 0.0000097752 1 0 6 d. 6.272 1 0 5 h. 44,252 1 0 4 RESEARCH LINKS 8. Write each of the following numbers in standard scientific notation. a. 1 e. (105 )(10 4 )(10 4 ) 0.00032 (10 2 ) B. Units b. 103 10 3 f. 43.2 (4.32 10 5 ) c. 103 10 3 g. (4.32 10 5 ) 432 d. 1 55,000 h. 1 (10 5 )(10 6 ) 9. Indicate the meaning (as a power of 10) for each of the following metric prefixes. a. kilo d. deci b. centi e. nano c. milli f. micro 10. Give the metric prefix that corresponds to each of the following: a. 1,000,000 d. 1 0 6 b. 1 0 3 e. 1 0 2 c. 1 0 9 f. 0.000001 C. Measurements of Length, Volume, and Mass 11. Which distance is greater, 100 mi or 100 km? 12. One liter of volume in the metric system is approximately equivalent to one in the English system. 13. The length 52.2 mm can also be expressed as cm. 14. Who is taller, a man who is 1.62 m tall or a woman who is 5 ft 6 in. tall? 15. A 1-kg package of hamburger has a mass closest to which of the following? a. 8 oz c. 2 lb b. 1 lb d. 10 lb 16. A 2-L bottle of soda contains a volume closest to which of the following? a. 5 gal c. 2 pt b. 1 qt d. 2 qt 17. A recipe written in metric units calls for 250 ml of milk. Which of the following best approximates this amount? a. 1 qt c. 1 cup b. 1 gal d. 1 pt 164 Chapter 5 Measurements and Calculations
18. Which metric system unit is most appropriate for measuring the distance between two cities? a. meters c. centimeters b. millimeters d. kilometers For exercises 19 and 20, some examples of simple approximate metric to English equivalents are given in the table. Examples of Commonly Used Units length mass volume A dime is 1 mm thick. A quarter is 2.5 cm in diameter. The average height of an adult man is 1.8 m. A nickel has a mass of about 5 g. A 120-lb woman has a mass of about 55 kg. A 12-oz can of soda has a volume of about 360 ml. A half gallon of milk is equal to about 2 L of milk. 19. What is the value in dollars of a stack of dimes that is 10 cm high? 20. How many quarters must be lined up in a row to reach a length of 1 meter? 5.2 Uncertainty in Measurement and Significant Figures A. Uncertainty in Measurement 21. When a measuring scale is used properly to the limit of precision, the last significant digit recorded for the measurement is said to be uncertain. Explain. 22. For the pin shown below, why is the third digit determined for the length of the pin uncertain? Considering that the third digit is uncertain, explain why the length of the pin is indicated as 2.85 cm rather than, for example, 2.83 or 2.87 cm. cm 1 2 3 23. Why can the length of the pin shown below not be recorded as 2.850 cm? cm 1 2 3 B. Significant Figures 2.8 2.9 1 2 3 4 5 6 7 8 9 24. Indicate the number of significant figures in each of the following: a. 1422 e. 200. b. 65,321 f. 2.00 1 0 2 c. 1.004 1 0 5 g. 435.662 d. 200 h. 56.341 25. Indicate the number of significant figures implied in each of the following statements: a. The population of the United States is 250 million. b. One hour is equivalent to 60 minutes. c. There are 5280 feet in 1 mile. d. Jet airliners fly at 500 mi/h. e. The Daytona 500 is a 500-mile race. 26. Round off each of the following numbers to three significant digits. a. 1,566,311 d. 0.0011672 b. 2.7651 1 0 3 e. 0.07759 c. 84,592 27. Round off each of the following numbers to the indicated number of significant digits, and write the answer in standard scientific notation. a. 0.00034159 to three digits b. 103.351 1 0 2 to four digits c. 17.9915 to five digits d. 3.365 1 0 5 to three digits 28. When the calculation (0.0043)(0.0821)(298) is performed, the answer should be reported to significant Chapter 5 Assessment 165
29. The quotient (2.3733 102 ) should be written (343) with significant 30. How many digits after the decimal point should be reported when the calculation (199.0354 43.09 121.2) is performed? 31. How many digits after the decimal point should be reported when the calculation (10,434 9.3344) is performed? 32. Evaluate each of the following, and write the a. 212.2 26.7 402.09 b. 1.0028 0.221 0.10337 c. 52.331 26.01 0.9981 d. (2.01 1 0 2 ) (3.014 1 0 3 ) 33. Evaluate each of the following, and write the a. (4.031)(0.08206)(373.1)/(0.995) b. (12.011)/(6.022 1 0 23 ) c. (0.500)/(44.02) d. (0.15)/(280.62) 34. Evaluate each of the following, and write the a. (2.0944 0.0003233 12.22)/(7.001) b. [(1.42 1 0 2 ) (1.021 1 0 3 )]/ (3.1 1 0 1 ) c. (9.762 1 0 3 )/[(1.43 1 0 2 ) (4.51 1 0 1 )] d. (6.1982 1 0 4 ) 2 5.3 Problem Solving and Unit Conversions A. Tools for Problem Solving 35. How many significant figures are understood for the numbers in the following definition: 1 mi 5280 ft? 36. Given that 1 mi 1760 yd, determine what conversion factor is appropriate to convert 1849 yd to miles and to convert 2.781 mi to yards. For exercises 37 and 38, apples cost $0.79 per pound. 37. What conversion factor is appropriate to express the cost of 5.3 lb of apples? 38. What conversion factor could be used to determine how many pounds of apples could be bought for $2.00? 39. Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case. a. 2.23 m to yards b. 46.2 yd to meters c. 292 cm to inches d. 881.2 in. to centimeters e. 1043 km to miles f. 445.5 mi to kilometers g. 36.2 m to kilometers h. 0.501 km to centimeters 40. Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case. a. 254.3 g to kilograms b. 2.75 kg to grams c. 2.75 kg to pounds d. 2.75 kg to ounces e. 534.1 g to pounds f. 1.75 lb to grams g. 8.7 oz to grams h. 45.9 g to ounces 41. If $1.00 is equivalent to 1.2 euros, what is $20.00 worth in euros? What is the value in dollars of 100 euros? 42. Boston and New York City are 190 miles apart. What is this distance in kilometers? In meters? In feet? 43. The United States will soon have high-speed trains running between Boston and New York capable of speeds up to 160 mi/h. Will these trains be faster or slower than the fastest trains in the United Kingdom, which reach speeds of 225 km/h? B. Temperature Conversions 44. The normal boiling point of water is F, or C. 45. On both the Celsius and Kelvin temperature scales, there are degrees between the normal freezing and boiling points of water. 166 Chapter 5 Measurements and Calculations
46. On which temperature scale ( F, C, or K) does 1 degree represent the smallest change in temperature? 47. Convert the following temperatures to kelvins. a. 155 C d. 101 F b. 200 C e. 52 F c. 52 C f. 196 F 48. Convert the following Kelvin temperatures to Celsius degrees. a. 275 K d. 77 K b. 445 K e. 10,000. K c. 0 K f. 2 K 49. Carry out the indicated temperature conversions. a. 40 C to Fahrenheit degrees b. 40 F to Celsius degrees c. 232 K to Celsius degrees d. 232 K to Fahrenheit degrees 50. Carry out the indicated temperature conversions. C. Density a. 201 F to kelvins b. 201 C to kelvins c. 351 C to Fahrenheit degrees d. 150 F to Celsius degrees 51. The ratio of an object s mass to its is called the density of the object. 52. A kilogram of lead occupies a much smaller volume than a kilogram of water because has a much higher density. 53. Typically, gases have very (high/low) densities compared with those of solids and liquids (see Table 5.8). 54. What property of density makes it useful as an aid in identifying substances? 55. Referring to Table 5.8, determine whether air, water, ethanol, or aluminum is the most dense. 56. For the masses and volumes indicated, calculate the density in grams per cubic centimeter. a. mass 4.53 kg; volume 225 c m 3 b. mass 26.3 g; volume 25.0 ml c. mass 1.00 lb; volume 500. c m 3 d. mass 352 mg; volume 0.271 c m 3 57. If 89.2 ml of a liquid has a mass of 75.2 g, calculate the liquid s density. 58. A cube of metal weighs 1.45 kg and displaces 542 ml of water when immersed. Calculate the density of the metal. 59. A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately 1.0 g/ml, will a block of material having a volume of 1.2 1 0 4 in. 3 and weighing 3.5 lb float or sink when placed in a reservoir of water? 60. The density of pure silver is 10.5 g/c m 3 at 20 C. If 5.25 g of pure silver pellets is added to a graduated cylinder containing 11.2 ml of water, to what volume level will the water in the cylinder rise? Use the information in the table for questions 61 62. Densities of Various Common Substances at 20 C Substance Physical State Density (g/c m 3 ) benzene liquid 0.880 salt (sodium chloride) solid 2.16 iron solid 7.87 silver solid 10.5 mercury liquid 13.6 gold solid 19.32 61. Calculate the volume of 50.0 g of each of the following substances. a. sodium chloride c. benzene b. mercury d. silver 62. Calculate the mass of 50.0 c m 3 of each of the following substances. a. gold c. lead b. iron d. aluminum Chapter 5 Assessment 167
Critical Thinking 63. Which unit of length in the metric system would be most appropriate in size for measuring each of the following items? a. the dimensions of this page b. the size of the room in which you are sitting c. the distance from New York to London d. the diameter of a baseball e. the diameter of a common pin 64. Suppose that your car is rated at 45 mi/gal for highway use and 38 mi/gal for city driving. If you wanted to write to your friend in Spain about your car s mileage, what ratings in kilometers per liter would you report? 65. You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches are 2.76 Euros per kilogram. Given that there are approximately 11.2 Euros to the dollar, calculate what a pound of peaches will cost in dollars. 66. Suppose a sample of antibiotic pills has a mass of 15.6 g. If the average mass per pill is 0.65 g, determine how many pills are in the sample. 67. For a material to float on the surface of water, the material must have a density less than that of water (1.0 g/ml) and must not react with the water or dissolve in it. A spherical ball has a radius of 0.50 cm and weighs 2.0 g. Will this ball float or sink when placed in water? (Note: Volume of a sphere 4 3 r3 ) 68. Ethanol and benzene dissolve in each other. When 100. ml of ethanol is dissolved in 1.00 L of benzene, what is the mass of the mixture? (See Table 5.8.) 69. For each of the following numbers, by how many places must the decimal point be moved to express the number in standard scientific notation? In each case, will the exponent be positive, negative, or zero? a. 55,651 d. 883,541 b. 0.000008991 e. 0.09814 c. 2.04 70. Which weighs more, 4.25 grams of gold or 425 milligrams of gold? 71. Indicate the number of significant figures in each of the following: a. This book contains over 500 pages. b. A mile is just over 5000 ft. c. A liter is equivalent to 1.059 qt. d. The population of the United States is approaching 250 million. e. A kilogram is 1000 g. f. The Boeing 747 cruises at around 600 mi/h. 72. An organic solvent has density 1.31 g/ml. What volume is occupied by 50.0 g of the liquid? 73. A sample containing 33.42 g of metal pellets is poured into a graduated cylinder initially containing 12.7 ml of water, causing the water level in the cylinder to rise to 21.6 ml. Calculate the density of the metal. 74. You place 10.00 ml of water in a graduated cylinder and add a 15.0 g sample of iron to the water. The new water level is 11.91 ml. What is the density of the iron? 75. You are a passenger in a car traveling at 55 mph (miles per hour). How many feet do you travel in 1 second? There are 5280 feet in a mile. 168 Chapter 5 Measurements and Calculations