180 CHAPTER 4 Systems of Numeration 80. Your Own System of Numeration Make up your own additive system of numeration and indicate the symbols and rules used to represent numbers. Using your system of numeration, write a) your age. Answers will vary. b) the year you were born. Answers will vary. c) the current year. Answers will vary. Recreational Mathematics 81. A Roman Numeral Equation Without using any type of writing instrument, what can you do to make the following incorrect equation a correct equation? Turn the book upside down. XI I X + = 82. Palindromes Words and numerals that read the same both backward and forward are called palindromes. Some examples are the words CIVIC and RACECAR, and the numerals 121 and 32523. Using Roman numerals, list the last year that was a palindrome. MM 83. Roman Numeral Years Which year in the past 2000 years required the most Roman numerals to write? Write out the year in Roman numerals. 1888, MDCCCLXXXVIII Research Activity 84. Egypt, China, and Greece In this section, we discussed the numeration systems of Egypt, China, and Greece. Choose one of these countries and write a paper that includes the following. a) State the current numerals used in your chosen country. b) Explain how that country’s current system of numeration works. If more than one system is used, discuss the system used most commonly. m Great Wall of China 85. Rhind Papyrus Write a report on the Rhind Papyrus (see the Did You Know on page 173). Include in your report some of the mathematics problems inscribed on the papyrus. In Exercises 53– 60, write the Hindu–Arabic numeral as a traditional Chinese numeral. 53. 53 * 54. 178 * 55. 378 * 56. 987 * 57. 4260 * 58. 6134 * 59. 7056 * 60. 8023 * In Exercises 61– 66, write the Ionic Greek numeral as a Hindu–Arabic numeral. 61. κ β 22 62. τ πα 381 63. ωοη 878 64. ∈ 905 65. βωπγ ι 2883 66. θσ λα ι 9231 In Exercises 67–72, write the Hindu–Arabic numeral as an Ionic Greek numeral. 67. 543 φμγ 68. 541 φμα 69. 784 ψ πδ 70. 2008 βη ι 71. 5005 ∈∈ ι 72. 9999 iu u In Exercises 73–76, write the numeral as numerals in the indicated systems of numeration. 73. in Hindu–Arabic, Roman, traditional Chinese, and Greek * 74. MCMXXXVI in Hindu–Arabic, Egyptian, Greek, and traditional Chinese * 75. in Hindu–Arabic, Egyptian, Roman, and Greek * 76. υκ β in Hindu–Arabic, Egyptian, Roman, and traditional Chinese * Concept/Writing Exercises 77. What is the difference between a number and a numeral? A number is a quantity, and it answers the question “How many?” A numeral is a symbol used to represent the number. 78. What is a system of numeration? A system of numeration consists of a set of numerals and a scheme or rule for combining the numerals to represent numbers. Challenge Problems/Group Activities 79. Write the Roman numeral for 999,999. CMXCIXCMXCIX *See Instructor Answer Appendix
RkJQdWJsaXNoZXIy NjM5ODQ=