210 CHAPTER 4 Systems of Numeration 57. base 5 33235 58. base 8 7178 59. base 12 32712 60. base 16 1CF16 65. 3024 4023 5 5 + 121025 66. 3407 7014 8 8 + 124238 61. + 121 322 4 4 11034 62. 10110 11001 2 2 + 1011112 63. + 9B 87 12 12 16612 64. + 2B9 456 16 16 70F16 4.4 In Exercises 61– 66, add in the base indicated. In Exercises 67–72, subtract in the base indicated. 67. − 321 133 4 4 1224 68. − 1001 101 2 2 1002 69. − A7B 95 12 12 9A612 70. − 4321 442 5 5 33245 71. − 1713 1243 8 8 4508 72. − F64 2A3 16 16 CC116 In Exercises 73–78, multiply in the base indicated. 73. × 431 3 6 6 21336 74. × 2321 3 4 4 202234 75. × 34 21 5 5 13145 76. × 476 23 8 8 136328 77. × 126 47 12 12 565612 78. × 1A3 12 16 16 1D7616 In Exercises 79–84, divide in the base indicated. 4.5 85. Multiply 125 23, × using the duplation and mediation method. 2875 86. Multiply 125 23, × using lattice multiplication. 2875 87. Multiply 125 23, × using Napier’s rods. 2875 79. ) 2 120 3 3 21 R1 3 3 80. ) 2 320 4 4 1304 81. ) 3 130 5 5 23 R1 5 5 82. ) 4 3020 6 6 4336 83. ) 3 2034 6 6 411 R1 6 6 84. ) 6 5072 8 8 664 R2 8 8 *See Instructor Answer Appendix In Exercises 25–28, write the Ionic Greek numeral as a Hindu–Arabic numeral. 25. πα 81 26. φμη 548 27. χ∈ 605 28. ' γ τ λδ 3334 In Exercises 29–32, write the Hindu–Arabic numeral as an Ionic Greek numeral. 29. 22 κ β 30. 773 ψογ 31. 867 ωξζ 32. 4219 δσ ιθ ι In Exercises 33–36, write the Babylonian numeral as a Hindu–Arabic numeral. 33. 191 34. 189 35. 3673 36. 7388 In Exercises 37– 40, write the Hindu–Arabic numeral as a Babylonian numeral. 37. 181 * 38. 3679 * 39. 7280 * 40. 36,184 * In Exercises 41– 44, write the Mayan numeral as a Hindu– Arabic numeral. 41. 48 42. 1367 43. 2521 44. 15,923 In Exercises 45– 48, write the Hindu–Arabic numeral as a Mayan numeral. 45. 69 * 46. 812 * 47. 1571 * 48. 17,913 * 4.3 In Exercises 49–54, convert the numeral to a numeral in base 10. 49. 478 39 50. 1112 7 51. 1304 28 52. 34257 1244 53. A9412 1552 54. 202203 186 In Exercises 55– 60, convert 463 to a numeral in the base indicated. 55. base 2 1110011112 56. base 4 130334
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