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Early Numeration Systems

Early Numeration Systems. Section 4.4. Early Numeration Systems. The Hindu-Arabic system was successful because it had just 10 symbols, including one for zero, and it was easy to compute in this base 10 system because it was a positional system.

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Early Numeration Systems

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  1. Early Numeration Systems Section 4.4

  2. Early Numeration Systems The Hindu-Arabic system was successful because it had just 10 symbols, including one for zero, and it was easy to compute in this base 10 system because it was a positional system. Let’s look at some early numeration systems that were not as successful. . .

  3. Egyptian Numeration System Ancient Egypt had several numeration systems; the oldest was a hieroglyphic notation developed around 3400 BC.

  4. World Geography Egypt

  5. Egyptian Numeration System Ancient Egypt had several numeration systems; the oldest was a hieroglyphic notation developed around 3400 BC. • It was a base 10 system. • It had no symbol for zero. • Egyptian hieroglyphics was NOT a positional system. It is an example of an additive system. Additive system – a numeration system in which the number represented is the sum of the values of all numerals

  6. Egyptian Numeration System

  7. Egyptian Numeration System Example Write 764 in the Egyptian system.

  8. Egyptian Numeration System Example Write 1352 in the Egyptian system.

  9. Egyptian Numeration System Example Write this in the Hindu-Arabic: 1,000,000 20,000 30 4 1,020,034 + ____4

  10. Egyptian Numeration System Example Write this in the Hindu-Arabic: 300,000 200 20 + ____2 2 300,222

  11. Roman Numeration System Roman numeration system was developed between 500 BC and 100 AD resulting from the tax collection and commerce.

  12. World Geography Roman Empire

  13. Roman Numeration System Roman numeration system was developed between 500 BC and 100 AD resulting from the tax collection and commerce. • There is no symbol for zero. • It was an additive system, base 10, with 7 symbols. • Latin letters were used for numbers. • It was used in Europe until 18thcentury. • It is still used today for outlines, clocks, and some page numbering.

  14. Roman Numeration System I V X L C D M 1 5 10 50 100 500 1000 I V X 1 5 10 I V 1 5 I 1 I V X L C 1 5 10 50 100 I V X L 1 5 10 50 I V X L C D 1 5 10 50 100 500 An overbar indicates 1000 and sidebars indicates  100. Memory Aid: IVALUE XYLOPHONES LIKE COWS DESIRE MILK Rules • If the smaller numeral is on the right, add. • If the smaller numeral is on the left, subtract. • Only the circled numerals can be subtracted. • Those circled can only be subtracted from the next two numerals greater than themselves. • Only one numeral can be subtracted at a time. • A letter can only be repeated 3 times consecutively.

  15. Roman Numeration System Example Write CLXVII as a Hindu-Arabic numeral. C L X V I I 100 50 10 5 1 1 100 + 50 + 10 + 5 + 1 + 1 = 167

  16. Roman Numeration System Example Write MCMXCVI as a Hindu-Arabic numeral. M C M X C V I 1000 100 1000 10 100 5 1 1000 + (1000 – 100) + (100 – 10) + 5 + 1 = 1996

  17. Roman Numeration System Example Write MCDXLVII as a Hindu-Arabic numeral. M C D X L V II 1000 100 500 10 50 5 11 1000 + (500 – 100) + (50 – 10) + 5 + 1 + 1 = 1447

  18. Roman Numeration System Example Write 249 as a Roman numeral. 40 = 10 + 10 + 10 + 10 = 50 – 10 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 200 = 100 + 100 = 500 – 100 – 100 – 100 = 50 + 50 + 50 + 50 9 = 5 + 1 + 1 + 1 + 1 = 10 – 1 = 1+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 2 4 9 not use same letter 3 times only subtract one not use same letter 3 times not use same letter 3 times C C XL I X

  19. Roman Numeration System Example Write 499 as a Roman numeral. 499 = 500 – 1 9 = 5 + 1 + 1 + 1 + 1 = 10 – 1 = 1+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 90 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 100 – 10 = 50 + 10 + 10 + 10 + 10 400 = 100 + 100 + 100 + 100 = 500 – 100 = 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50 4 9 9 only subtract from next 2 bigger not use same letter 3 times not use same letter 3 times not use same letter 3 times C D X C I X

  20. Traditional Chinese Numeration System The Chinese people use Hindu-Arabic numerals for convenience and traditional Chinese numerals for formal situations and money.

  21. World Geography China

  22. Traditional Chinese Numeration System The Chinese people use Hindu-Arabic numerals for convenience and traditional Chinese numerals for formal situations and money. • It reflects the way numbers are spoken. Thus it is considered an additive system. • It is a base 10 system with lots of symbols (though only 12 common) with a rarely used zero symbol. • It is also used by Japanese, Korean and Vietnamese. • Some numerals date back to 14th century BC. The system is as old as Babylonian and Egyptian systems.

  23. Traditional Chinese Numeration System

  24. Traditional Chinese Numeration System Example Write 3,264 as a traditional Chinese numeral. 3 1000 + 2  100 + 6  10 + 4  1 = 3 1000 + 2  100 + 6  10 + 4  1 = Chinese numbers are written vertically and read from top. There is a symbol for 4, so the place value is NOT needed. Write numeral and then the place value it is multiplied by.

  25. Traditional Chinese Numeration System Example Write 8,005 as a traditional Chinese numeral. 8 1000 + 5=

  26. Traditional Chinese Numeration System Example Write 2,693 as a traditional Chinese numeral. 2 1000 + 6  100 + 9  10 + 7 =

  27. Traditional Chinese Numeration System Example Write this traditional Chinese numeral as Hindu-Arabic. 4 400 2 20 5 + __5 425

  28. Traditional Chinese Numeration System Example Write this traditional Chinese numeral as Hindu-Arabic. 7 7,000 3 300 + 6 6 7,306

  29. Ionic Greek Numeration System Was developed about 450 BC in Greece and islands/coastland around the Ionian Sea.

  30. World Geography Greece Ionian Sea

  31. Ionic Greek Numeration System Was developed about 450 BC in Greece and islands/coastland around the Ionian Sea. • Greek letters were used for numerals, written horizontally in descending order. • There are more than 24 symbols, but no consistent symbol for zero. It is a base 10 system. • It is an additive system. • Ionic Greek numerals are used now as ordinal numbers (1st, 2nd, 3rd, etc.) and situations similar to where Roman numerals are used. Else Hindu-Arabic is used.

  32. Ionic Greek Numeration System

  33. Ionic Greek Numeration System Example Write 21 as an Ionic Greek numeral. a k 21 = 20 + 1

  34. Ionic Greek Numeration System Example Write 853 as an Ionic Greek numeral. 853 = 800+ 50 + 3 g n w

  35. Ionic Greek Numeration System Example Write yld as an Ionic Greek numeral. 700 y l d 30 4 + 4 734

  36. Ionic Greek Numeration System Example Write fpeas an Ionic Greek numeral. 500 f p e 80 5 + 5 585

  37. Homework From the Cow book 4.1 pg 168 # 1 – 49 EOO, 61, 62 4.2 pg 175 # 1 – 37 EOO, 49 4.3 pg 181 # 1 – 33 EOO, 35, 37 4.4 pg187 # 1 – 53 EOO, 64 – 66 all NOTE: EOO means “every other odd” NOTE: Tables for Egyptian, Roman, Chinese, and Ionic Greek numerals are found in section 4.4 of the textbook. These will not have to be memorized for the test.

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