EXERCISE 49 DRILL WORK IN DECIMALS 1. Why will there be three decimal places in the product of 0.75 multiplied by 0.3? of 2.325 multiplied by 7 ? Exs. 1-9 illustrate the oral work that should be given frequently. Without multiplying, state the number of decimal places in each of the following products : 2. 2.8 x 7.9. 4. 2.007 x 6.09. 6. 1.203 x 2.67. 3. 1.7 x 1,42. 5. 1.234 x 3.456. 7. 3.421 x 0.713. 8. Multiply 1.21 by 2; by 3; by 4; by 10; by 100. 9. Divide 1.05 by 5; by 10; by 2; by 3; by 0.1. Add the following, timing yourself : 24. 32.78 45.67 6.35 842.38 682.73 42.07 327.29 102.93 189.27 420.63 41.52 25. 608.72 Copy and subtract, timing yourself : 26. $640.00 – $298.29. 29. $702.53 – $129.65. 27. $902.63 - $127.49. 30. $1000.00 – $298.75. 28. $3476.42 - $1029.29. 31. $2025.30 – $1627.92. Multiply the following : 32. 234.5 by 8.001. 35. 0.500 by 0.600. 33. $683.45 by 0.2. 36. $281.42 by 6.50. 34. $283.75 by 42.8. 37. $333.33} by 0.3. 38. At $17.52 a front foot, what will a piece of land of 28.334 feet front cost? 39. A tank when full holds 42.8 gallons of water. How much does it contain when 0.37 full ? 40. A certain rectangle is 0.78 as wide as it is long. It is 4.9 inches long. What is the perimeter ? 41. A certain rectangle is 3.42 times as long as it is wide. It is 4.8 feet wide. What is the perimeter ? 42. A city lot is 45.8 feet by 76.3 feet. What is the area of the lot? What is it worth at $1.50 a square foot ? 43. If the circumference of a circle is 3.1416 times the diameter, what is the circumference of a circle the diameter of which is 42.27 feet? 44. At $1.75 each, what will 17 books cost? 45. Find the perimeter of a square 34.7 feet on a side. 46. At $75.50 an acre, what will 25.5 acres of land cost ? 47. At $0.75 a yard, what will 32.2 yards of silk cost? 48. At $125 a front foot, how much will a city lot cost having a frontage of 72.3 feet? Multiply: 49. 1.4 x 6.64. 59. 6.81 x 7.92. 69. 30.5 x 57.2. 50. 3.6 x 19.72. 60. 8.35 x 6.423. 70. 8.25 x 6.37. 51. 43.2 x 98.6. 61. 89.1 x 49.3. 71. 68.7 x 40.5. 52. 0.823 x 2946. 62. 72.9 x 87.09. 72. 53.6 x 2.889. 53. 48.1 x 32.5. 63. 20.5 x 60.7. 73. 43.7 x 74.1. 54. 26.8 x 80.8. 64. 20.2 x 20.2. 74. 1.6 x 140.64. 55. 60.9 X 90.6. 65. 73.7 x 73.7. 75. 6.2 x 53.134. 56. 4.72 x 6.93. 66. 42.3 x 5.37. 76. 17.2 x 26.35. 57. 2.87 x 5.492. 67. 1.5 x 553.35. 77. 2.175 x 6.73. 58. 16.4 x 17.25. 68. 5.8 x 439.002. 78. 0.273 x 0.625. Divide : 79. 17.25 : 500. 84. $32.48 • 8. 80. 817.6 : 700. 85. $26.25 · 25. 81. 0.7364 : 7000. 86. $21.42 : 18. 82. 3.248 ; 200. 87. $99.54 + 14. 83. 82.48 ; 8000. 88. $82.20 : 12. 89. 20.720 : 0.28. 90. 38.8692 ; 5.4. 91. 825.468 ; 4.2. 92. 888.16 : 2.8. 93. 1131.264 : 4.8. In the following divisions, carry the quotient to three decimal places : 94. 17.78 : 1.5. 97. 167.8 ; 3.7. 100. 19.26 ; 3.1. 95. 423.6 : 0.27. 98. 62.23 : 0.23. 101. 8.348 ; 2.68. 96. 976.34 : 0.125. 99. 483.62 = 42.7. 102. 826.3 : 12.5. CHAPTER VII DENOMINATE NUMBERS 98. Denominate Number. A concrete number that expresses measure called a denominate number. For example, $7 and 2 feet 3 inches are denominate numbers, but not 5 chairs or 8 rivers. 99. Compound Number. A denominate number involving two or more different units is called a compound number. For example, 2 feet 3 inches, or 3 hours 20 minutes. We do not usually speak of $2.50 as a compound number because it is written as an integer and a decimal fraction. If we should write 27 feet or 2.25 feet instead of 2 feet 3 inches, we should not be using compound numbers. Some work in compound numbers is done in the primary grades, and many of the common measures are therefore already known. 100. Measures of Length. The table of common measures of length is as follows: 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 5 yards, or 162 feet = 1 rod (rd.) 320 rods, or 5280 feet: 1 mile (mi.) A hand (4 in.) is used in measuring the height of horses; a fathom (6 ft.) and cable length (120 fathoms) in measuring depths of water; a knot (nautical mile, 1.152 common or statute miles, or 6080.27 ft.) in measuring distances at sea. Carpenters and mechanics usually write 2' 6" for 2 ft. 6 in. 101. Reduction. The process of changing the unit of a number without changing the value is called reduction. Thus 2 ft. 6 in. = 30 in. 2.5 ft. ft. in. 102. Reduction Descending. Reduction from a higher to a lower denomination is called reduction descending. For example, required to reduce 2 ft. 3 in. to 2 3 inches. 12 1 ft. = 12 in., 24 2 ft. = 2 x 12 in. 3 = 24 in. Therefore 24 in. + 3 in. = 27 in. 27 For convenience the actual multiplications and additions are carried out as shown at the right. In practical life we seldom have reductions involving more than two different units (denominations), and in this arithmetic other cases will not in general be considered. Therefore, in reduction descending, multiply the number of the highest denomination given, by the number showing how many units of the next lower denomination are equal to one of the higher. To the product add the given number of this lower denomination. Proceed thus with each successive result until the required denomination is reached. EXERCISE 50 Reduce : 1. 54 ft. 7 in. to inches. 10. 160 rd. to yards. 2. 72 ft. 9 in. to inches. 11. 5 mi. to rods. 3. 28 yd. to feet; to inches. 12. 7 mi. to yards. 4. 54 yd. to feet; to inches. 13. 224 mi. to rods. 5. 26 rd. to yards; to feet. 14. 3.25 mi. to feet. 6. 320 rd. to yards; to feet. 15. 0.5 mi. to feet. 7. 41.8 mi. to miles and feet. 16. 0.6 mi. to feet. 8. 25.75 mi. to miles and feet. 17. 0.65 mi. to feet. 9. 126.7 mi. to miles and feet. 18. 0.01 mi. to yards. 19. A knot being 1.152 miles, how many miles does a ship sail in going 480 knots ? |