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Section 4.1

Section 4.1. The Evolution of Numeration Systems. Objectives. Understand and use the Egyptian System. Understand and use the Roman system. Understand and use the Chinese system. Understand and use the Ionic Greek system. Key Terms. Number: tell us how many objects we are counting.

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Section 4.1

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  1. Section 4.1 The Evolution of Numeration Systems

  2. Objectives • Understand and use the Egyptian System. • Understand and use the Roman system. • Understand and use the Chinese system. • Understand and use the Ionic Greek system.

  3. Key Terms • Number: tell us how many objects we are counting. • Numeral: a symbol which represents a number. • System of Numeration: a set of basic numerals and rules for combining them to represent numbers. • Hindu-Arabic Numerals: a system of writing numerals that were invented in India and brought to Europe by Arabs, which we use today.

  4. Hindu-Arabic System • An important characteristic of our Hindu-Arabic system is that we can write the numeral for any number, large or small, using only ten symbols. • The ten symbols are as follows:0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. • These symbols are called digits.

  5. Egyptian Hieroglyphic System

  6. Example 1: • Convert to Hindu-Arabic Notation

  7. Example 2: • Convert to Hindu-Arabic Notation

  8. Example 3: • Convert to Hindu-Arabic Notation

  9. Example 4: 1,320,401 • Convert to Egyptian Hieroglyphics

  10. Example 5: 421,536 • Convert to Egyptian Hieroglyphics

  11. Example 6: 1,752 • Convert to Egyptian Hieroglyphics

  12. Example 7: • Adding in the Egyptian System.

  13. Example 8: • Adding in the Egyptian System.

  14. Example 9: • Subtracting in the Egyptian System

  15. Example 10: • Subtracting in the Egyptian System

  16. Section 4.1 Assignment I • Classwork: • TB pg. 204/1 – 24 All • Must write problem and show ALL work to receive credit for this assignment.

  17. Section 4.1 The Evolution of Numeration SystemsPart II

  18. Egyptian Method of Doubling

  19. Example 11: 13 X 43 • Doubling Method

  20. Example 12: 35 X 21 • Doubling Method

  21. Roman Numerals NOTE: See pg. 202 in TB

  22. Example 13: MCMXCVI • Convert to Hindu-Arabic

  23. Example 14: MCDXLVII • Convert to Hindu-Arabic

  24. Example 15: 931 • Convert to Roman Numerals

  25. Example 16: 87,423 • Convert to Roman Numerals

  26. Section 4.1 Assignment II • Classwork: • TB pg. 205/ • Must write problem and show ALL work to receive credit for this assignment.

  27. Section 4.1 The Evolution of Numeration SystemsPart III

  28. Chinese Number System

  29. NOTE: • The Chinese did not have a symbol for the zero in the traditional notation, and they did not use the concept of place value. So they had to specify whether they were talking about 6 tens, 6 hundreds, or 6 thousands, etc. • This required an extra symbol.

  30. Example 17: • Translate to Hindu-Arabic

  31. Example 18: • Translate to Hindu-Arabic

  32. Example 19: • Translate to Hindu-Arabic

  33. Example 20: 87 • Translate to Chinese

  34. Example 21: 358 • Translate to Chinese

  35. Example 22: 3264 • Translate to Chinese

  36. Section 4.1 Assignment III • Classwork: • TB pg. 205/59 – 72 All • Must write problem and show ALL work to receive credit for this assignment.

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