CHAPTER EIGHT THE METRIC SYSTEM

CHAPTER EIGHT THE METRIC SYSTEM Exercise Set 8.1 1. The metric system. 2. The U.S. customary system. 3. It is the worldwide accepted standard of measurement. There is only 1 basic unit of measurement for each quantity. It is based on the number 10 which makes many calculations easier. 4. a) meter b) kilogram c) liter d) celsius. a) Move the decimal point one place for each change in unit of measure. 714.6 b) 714.6 cm = km = 714.6 x 10 - km = 0.007146 km 10 c) 30.8 hm = (30.8)(1000) dm = 30800 dm 6. a) mega b) micro 7. kilo 1000 times the base unit k hecto 100 times the base unit h deka 10 times the base unit da dec 1/10 times the base unit d centi 1/100 times the base unit c milli 1/1000 times the base unit m 8. a) 10,000 times greater b) 1 h = 10,000 cm c) 1 cm = 0.0001 hm. a) 100 times greater b) 1 dam = 100 dm c) 1dm = 0.01 dam 10. a) 0 o C b) 100 o C c) 37 o C 11. 2 pounds 12. 1 yard 13. grams 14. 30 o C 1. 22 o C 16. 2 m. 17. kilo d 18. milli b 1. hector c 20. deka e 21. deci f 22. centi a 23. a) 10 liters b) 1/100 liter c) 1/1000 liter d) 1/10 liter e) 1000 liters f) 100 liters 24. a) 100 grams b) 0.001 gram c) 1000 grams d) 0.01 gram e) 10 grams f) 0.1 gram 2. mg 1/1000 gm 26. cg 1/100 gm 27. dg 1/10 gm 28. dag 10 gm 2. hg 100 gm 30. kg 1000 gm 31. Max. load 320 kg = (320 x 1,000) g = 320 000 g 32. Max. load 320 kg = (320 x 1,000,000) mg = 320,000,000 mg 33. 2 m = (2 x 100) cm = 200 cm 34. 3.7 hg = (3.7 x 100) g = 3,70 g 27

280 CHAPTER 8 The Metric System 3. 0.0 hl = (0.0)(100) =. l 36. 7 dam = (7 x 10) m = 70 m 37. 242.6 cm = (242.6)(0.0001) hm = 0.02426 hm 38. 1.34 ml = (1.34)(0.001) l = 0.00134 l 3. 4036 mg = (4036)(0.00001) hg = 0.04036 hg 40. 14.27 kl = (14.27)(1000) l = 14 270 l 41. 1.34 hm = (1.34)(10000) cm = 13,400 cm 42. 0.000062 kg = 62 mg 43. 2. kg = 2,00 g 44. 7.3 m = 7300 mm 4. 8 l = 8,000 ml 46. 24 dm = 0.0024 km 47. 240 cm = 0.0240 hm 48. 6,04 mm = 6.04 m 4. 40,302 ml = 4.0302 dal 0. 0.034 ml = 0.00034 l 1. 0 cm,.1 dam, 0.47 km 2. 680 m, 14 hm, 62 km 3. 2.42 kg, 2,400 g, 24,300 dg 4. 420 cl, 4.3 l, 0.04 kl. 203,000 mm, 2.6 km, 2.6 hm 6. 0.032 kl, 460 dl, 48,000 cl 7. Jim, since a meter is longer than a yard. 8. 1 hectometer in 10 min. 1 hm > 1 dm. The pump that removes 1 dal of water per min. 1 dekaliter > 1 deciliter 61. a) Perimeter= 2l + 2w= 2(74) + 2()= 346 cm b) 346 cm = (346 x 10) mm = 3,460 mm 63. a) (4)(27 m) = 108 m b) 108 m = 0.108 km c) 108 m = 108 000 mm 6. 8 (400) m = 3,200 m; 3,200 m = 3.2 km 67. a) 6(360) ml = 2,160 ml b) 2160(1000) = 2.16 l c) 2.4 / 2.16 = $1.13 per liter 6. a) (6.)(1000) = 6,00 gm b) 6,00 / 3 = 2300 gm 2300 gm = 23,000 dg 60. The side with the 1 lb. weight would go down. kg = (2.2 lbs.) = 11 lbs. 62. a) (2)(20)(7) = 3,00 mg / week b) 3,00 mg / week = 3. g / week 64. a) 1,200 km / 187 l = 6.417 km/l b) 1,200,00 / 187 l = 6,417 m/l 1000 ml 1 min 66. 360 l = (360 l) 1 l 360 ml = 83.333 min. or 1 hr 23.333 min. 68. ($ 1.03)(37.7 l) = $ 38.83 70. 70 km = 700 hm 70 32. = 717. km 71. 1 gigameter = 1000 megameters 72. 1 nanogram =.001 microgram 73. 1 teraliter = 1 x 10 24 picoliters 74. 1 megagram = 1 x 10 1 nanogms 7. 0.8/.027 = 2.6 30 eggs 76. 0.8/.288 = 2.777 2.8 cups 77. 1 mg = 0.1 g 78. 1.6 mg = 0.0016 g 7. 000 cm = dam 0.8/0.1 = 4.1 cups 0.8/0.016 = 00 00(4) = 24,00 g 80. 2000 mm = 2 m 81. 0.00006 hg = 6 mg 82. 3000 dm = 3 hm 83. 0.02 kl = 2 dal 84. 00 cm = m 8. magr gram 86. migradec decigram 87. rteli liter 88. raktileed dekaliter 8. terem meter 0. leritililm milliliter 1. reketolim kilometer 2. timenceret centimeter 3. greeed sulesic degree celsius 4. togmeharc hectogram

SECTION 8.2 281 Exercise Set 8.2 1. volume 2. length 3. area 4. length. volume 6. volume 7. volume 8. volume. area 10. volume 11. length 12. area 13. Answers will vary. 14. Answers will vary. 1. Answers will vary. 16. Answers will vary. (AWV) 17. Answers will vary. 18. Answers will vary. 1. 1 cubic decimeter 20. 1000 l = 1 kiloliter 21. 1 cubic centimeter 22. square kilometers 23. area 24. 2. acres 2. centimeters 26. kilometers 27. cm or mm 28. centimeters 2. centimeters 30. millimeters 31. millimeters 32. meters 33. cm or mm 34. cm or mm 3. kilometers 36. cm or m 37. c 27 m 38. a 2 cm x 3 cm 3. c km 40. a 160 cm 41. a 2 cm 42. b 8 cm 43. a 3 dam 44. c 37 m 4. mm AWV 46. cm AWV 47. cm or m AWV 48. mm or cm AWV 4. mm or cm AWV 0. mm AWV 1. cm, km 2. km 3. m 4. m. cm 6. km 7. sq. mm. or sq. cm. 8. hectares or sq. km.. sq. m. 60. sq. mm. or sq. cm. 61. sq. m. or hectares 62. sq. m. or hectares 63. sq. mm. or sq. cm. 64. sq. cm. or sq. m. 6. hectares or sq. km. 66. sq. m. 67. b 2.2 sq.m. 68. a sq. cm. 6. a 800 sq. m. 70. b 1/8 ha 71. c 360 sq. cm. 72. a 2. sq. cm. 73. c 1200 sq. mm. 74. c 400 sq. km. 7. AWV 76. AWV 77. AWV 78. AWV 7. AWV 80. AWV 81. kiloliters 82. liters 83. milliliters 84. cubic centimeters 8. liters 86. cubic meters 87. cubic meters 88. cubic meters 8. liters 0. cubic meters 1. c 7780 cu. cm. 2. a 0. cu. m. 3. c kl 4. b 3 ml. a 0 cu. m. 6. b 120 ml 7. a 24 cu. m. 8. b 14,000 cu. cm.. a) 144,000 cc. b) 12,61 cc 100. a) AWV b) (2)(1.)(.2) =.7 m 3 101. a) AWV b) v (3.14)(0.2) 2 (1) = 0.20 m 3 102. a) AWV b) v =π r 2 h (3.14)(0.20) 2 (2) = 0.2m 3 103. a) AWV b) A = lw = (4)(2.2) = 8.8 cm 2 104. A = π r 2 = (3.14)(1.2) 2 = 4.216 cm 2 10. (82)(62) - (0)(42) = 084-2100 = 284 cm 2 106. a) (73)(3) = 386 m 2 107. a) (3.7)(1.4) =.2 km b) 386 (70)(0) = 386 300 = 86 m 2 b) (.2)(100 ha) = 2 ha 108. a) (22.)(18.3) = 411.7 m 2 10. a) (18)(10)(2.) = 40 m 3 b) (411.7)(0.0001 ha) = 0.04117 ha b) 40 m 3 = 40 kl 110. Total Surface Area of 4 walls = 2lh + 2wh = 2(20)(6) + 2(12)(6) = 384 m 2 Liters for first coat = (384 m 2 1 l ) 2 10 m = 38.4 l Liters for second coat = (384 m2 1 l ) 2 1 m = 2.6 l Total liters = 38.4 + 2.6 = 64 l Total cost = (64)($4.7) = $304

282 CHAPTER 8 The Metric System 111. a) V = lwh = (70)(40)(20) = 6,000 cm 3 b) 6,000 cm 3 = 6,000 ml c) c) 6 000 ml = 6000 1000 l = 6 l 112. V = π r 2 h (3.14)(4.0) 2 (12.) 113. 10 2 = 100 times larger 114. 100 2 = 10,000 times larger 628 cm 3 11. 10 3 = 1000 times larger 116. 10 3 = 1000 times larger 117. 1,000,000 mm 2 118. 1,000,000,000 cm 2 11. 100 hm 2 120. 0.0001 m 2 121. 0.000,000,000,1 hm 2 122. 10,000 mm 2 123. 1,000,000 cm 3 124. 1 hm 3 = 0.001 km 3 12. 43 cm 3 = 43 ml 126. 43 cm 3 = 0.43 l 127. 76 kl = 76 m 3 128. 4.2 l = 4,200 cm 3 12. (6.0 x 10 4 )(10) = 600,000 dl 130. (600,000)(100) = 60,000,000 ml = 60,000,000 cc 131. AWV 132. AWV 133. 6.7 kl = 6.7 m 3 = (6.7 x 10 3 ) dm 3 = 6,700 dm 3 134. 1.4 ha = 14,000 m 2 = (14000 x 100 2 ) cm 2 = 140,000,000 cm 2 13. a) 1 sq mi = (1 mi 2 )(280) 2 2 ft mi 2 = 27,878,400 ft 2 27,878,400 ft 2 x (12) 2 2 in = 4,014,48,600 in 2 2 ft b) It is easier to convert in the metric system because it is a base 10 system. 136. a) (1 yd 3 ) = (36 in) 3 = 46,66 in 3 (46,66 in 3 )(6) = 27,36 in 3 b) It is easier to convert in the metric system because it is a base 10 system. 137. Answers will vary. 138. a) 1. m = 10 cm 10 0 = 100 cm. b) 10/0 = 3 3 times larger c) No. 13. a) 10.7 liters / day b) 43.2 liters / day Exercise Set 8.3 1. kilogram 2. gm 3. 2 lb 4. metric tonne. approx. 3 o C AWV 6. approx. 1 o C AWV 7. Answers will vary AWV 8. 8.a) Yes; mass is a measure of the amount of matter in an object. b) No; weight is a measure of gravitational force.. kilograms or grams 10. kilograms 11. grams 12. kilograms or grams 13. grams 14. metric tonnes 1. metric tonnes 16. milligrams 17. grams 18. grams 1. b 2.26 kg 20. a.1 mg 21. b 1.4 kg 22. c 0.4 kg 23. b 2800 kg 24. c 1.6 t 2. AWV 26. AWV 27. AWV 28. AWV 2. c 0 o C 30. c 0 o C 31. b 27 o C 32. b Dress warmly and walk.

SECTION 8.3 283 33. b o C 34. c bathing suit 3. c 177 o C 36. c 1260 o C 37. b -7 o C 38. c 40 o C 3. F = (30) + 32 = 4 + 32 = 86 o F 40. F = ( ) + 32 = + 32 = 23o F 41. C = (2 32) 43. C = (180 32) = (60) = (148) = 33.3 o C 42. C = ( 10 32) = ( 42) = 23.3o C = 82.2 o C 44. C = (8 32) = (66) = 36.7 o C 4. F = (37) + 32 = 66.6 + 32 = 8.6 o F 46. F = ( 4) + 32 = 7.2 + 32 = 24.8o F 47. C = (13 32) = ( 1) = 10.6o C 48. C = (7 32) = (43) = 23. o C 4. F = (4) + 32 = 81 + 32 = 113 o F 0. F = (60) + 32 = 108 + 32 = 140 o F 1. C = ( 20 32) = ( 2) = -28.o C 2. C = (42 32) = (33) 3. F = (22). F = (3.1) = 218.3 o C + 32 = 3.6 + 32 = 71.6 o F 4. F = (1.6) + 32 = 28.1 + 32 = 60.1 o F + 32 = 63.2 + 32 =.2 o F 6. F = (32.3) + 32 = 8.1 + 32 = 0.1 o F 7. low: F = (17.8) + 32 = 32 + 32 = 64.04 o F high: F = (23.) + 32 = 42.3 + 32 = 74.3 o F Range = 74.30 64.04 = 10.26 o F 8. low: F = (22) + 32 = 3.6 + 32 = 71.6 o F high: F = (34) + 32 = 61.2 + 32 = 3.2 o F Range = 3.2 71.6 = 21.6 o F. cost = (6.2)(.70) = $ 4.34 60. cost = (1.3)(.80) = $ 1.04 61. total mass = 4 g + 2 g + 370 ml = 4 g + 2 g + 370 g = 444 g 63. a) V= lwh, l = 16 m, w = 12 m, h = 12 m V = (16)(12)(12) = 2304 m 3 b) 2304 m 3 = 2304 kl c) 2304 kl = 2304 t 62. fuel used = (4320)(17) = 73,440 kg 1 t 73,440 kg 1000 kg = 73.44 t 64. a) V = π r 2 h r = 0 cm = 0.0 m h = 10 cm = 1. m V = (3.14)(0.0) 2 (1.0) = 1.177 m 3 b) 1.177 m 3 = 1.177 kl = 1177. l c) 1177. l = 1177. kg 1 t 1000 kg 6. 4.2 kg = (4.2 kg) = 0.0042 t 66..2 t = (.2 t) = 20 kg 1000 kg 1 t 1000 kg 1 t 67. 17.4 t = (17.4 t) = 17,400 kg = 68. 1,460,000 mg = 1.46 kg = (1.46 kg) 1 t = 1000 kg 17,400,000 g 0.00146 t

284 CHAPTER 8 The Metric System 6. Yes, 78 o F = (78 32) 2.6o C, not 20 o C 70. Normal body temperature is 8.6 o F or 37 o C. Maria's temperature is 38.2 o C which is above normal. She should take an aspirin. 71. 1.2 l = 1200 ml a) 1200 gm b) 1200 cm 3 72. 40 o C = ( 40) + 32 = 72 + 32 40o F 73. a) V = lwh l = 1 yd = 3 ft w = 1 in = 1.2 ft h = 1. ft V = (3)(1.2)(1.) =.62 cubic feet b) (.62 ft 3 lbs ) 62. ft 3 = 31.6 lb 1 gal c) (31.6 lb) = 42.4 gal 8.3 lb 74. 3 kg x (3)(2) = 6 = 4x x = 6/4 = 3/2 = 1. 1. kg = 100 g 1. kg 7. a) -62.11 o C F = ( 62.11) + 32 = -111.78 + 32 = -7.78o F b) 2. o C F = (2.) + 32 = 4. + 32 = 36. o F c) 18,000,000 o F C = (18, 000, 000 32) = (17,, 68) = 0,,82.2 10,000,000 o C