4.2 Place-Value or Positional-Value Numeration Systems 187 5. In the numeral 234, the 4 represents 4 _______. Units 6. The Babylonian system is not considered a true place-value system because it lacked a symbol for ________. Zero 7. In the Babylonian numeration system, a) the symbol represents the number ________. 1 b) the symbol represents the number ________. 10 c) the symbol indicates ________. Subtraction 8. The base used in the Babylonian numeration system is ________. 60 9. In the Mayan numeration system, a) the symbol represents the numeral ________. 0 b) the symbol represents the numeral ________. 1 c) the symbol represents the numeral ________. 5 10. It is believed that the Mayans used 18 20 × instead of 202 so that their numeration system would conform to their ________, which had 360 days. Calendar Practice the Skills In Exercises 11–18, write the Hindu–Arabic numeral in expanded form. 11. 43 (4 10) (3 1) × + × 12. 68 (6 10) (8 1) × + × 13. 975 (9 100) (7 10) (5 1) × + × + × 14. 822 (8 100) (2 10) (2 1) × + × + × 15. 4387 (4 1000) (3 100) (8 10) (7 1) × + × + × + × 16. 3769 * 17. 16,402 * 18. 3,765,934 * In Exercises 19–26, write the Babylonian numeral as a Hindu–Arabic numeral. 19. 14 20. 19 21. 677 22. 1153 23. 4868 24. 29,891 25. 36,002 26. 104,418 In Exercises 27–34, write the Hindu–Arabic numeral as a Babylonian numeral. 27. 23 * 28. 38 * 29. 129 * 30. 471 * 31. 11,958 * 32. 12,435 * 33. 3605 * 34. 64,813 * In Exercises 35– 42, write the Mayan numeral as a Hindu–Arabic numeral. 35. 57 36. 207 37. 2707 38. 930 39. 4000 40. 4682 41. 7211 42. 17,284 In Exercises 43–50, write the Hindu–Arabic numeral as a Mayan numeral. 43. 16 44. 77* 45. 406 * 46. 886* 47. 2163 * 48. 5764* 49. 21,948* 50. 30,967 * In Exercises 51 and 52, write the numeral in the indicated systems of numeration. 51. in Hindu–Arabic and Babylonian * 52. in Hindu–Arabic and Mayan * Concept/Writing Exercises 53. Describe two ways that the Mayan place-value system differs from the Hindu–Arabic place-value system. The Mayan system has a different base and the numerals are written vertically. 54. a) The Babylonian system did not have a symbol for zero. Why did this lead to some confusion? * b) Write 133 and 7980 as Babylonian numerals. * Challenge Problems/Group Activities 55. a) Write the Mayan numeral for 999,999. * b) Write the Babylonian numeral for 999,999. * *See Instructor Answer Appendix
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