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THE NUMERATION SYSTEM

THE NUMERATION SYSTEM. Prepared By: Still John F. Reyes. ANCIENT NUMERATION SYSTEMS. Early numeration system dates back to roughly 3500 B.C. The Egyptians are among those who have developed their own system.

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THE NUMERATION SYSTEM

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  1. THE NUMERATION SYSTEM Prepared By: Still John F. Reyes

  2. ANCIENT NUMERATION SYSTEMS • Early numeration system dates back to roughly 3500 B.C. • The Egyptians are among those who have developed their own system. • The Rhind Papyrus, a manuscript written in about 1650 B.C. presents a comprehensive description of Egyptian arithmetic. It was based on pictures of objects.

  3. THE EGYPTIAN NUMERATION SYSTEM • The Egyptians used the oldest numeration system called hieroglyphic notation.

  4. Example 1: Using the Egyptian Numeration System Write the following numeral as a Hindu-Arabic numeral: Solution:Using the table, find the value of each of the Egyptian numerals. Then add them. 1,000,000 + 10,000 + 10,000 + 10 + 10 + 10 + 1 + 1 + 1 + 1 = 1,020,034

  5. Example 2: Using the Egyptian Numeration System Write 1752 as an Egyptian numeral. Solution:First break down the Hindu-Arabic numeral into quantities that match the Egyptian numerals: 1752 = 1000 + 700 + 50 + 2 = 1000 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 10 + 10 + 10 + 10 + 10 + 1 + 1 Now use the table to find the Egyptian symbol that matches each quantity. Thus, 1752 can be expressed as

  6. Babylonian Numeration System • Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. • This system first appeared around 3100 B.C.

  7. Babylonian Numerals

  8. It uses only two numerals or symbols, a one and a ten to represent numbers and they looked like these To represent numbers from 2 to 59, the system was simply additive.

  9. Example #1:5 is written as shown: 12 is written as shown:

  10. Notice how the ones, in this case two ones are shown on the right just like the Hindu-Arabic numeration system 45 is written as shown:

  11. For number bigger than 59, the Babylonian used a place value system with a base of 60 62 is written as shown: Notice this time the use of a big space to separate the space value

  12. The Greek Numeration System • The Greek numeration system appears to have extended from roughly 600 B.C. to A.D. 100. • The Greeks used 27 letters to represent numbers

  13. The Greek Numeration System

  14. Example: Using the Ionic Greek Numeration System • Write ψλδ as a Hindu-Arabic numeral. Solution: • Retrieving what each Greek numeral represents, ψ =700, λ=30, δ=4, next we add the digits left to right according to their positions. ψλδ = 700 + 30 + 4 = 734 • Thus, ψλδ represents 734 in Hindu-Arabic numerals.

  15. Roman Numeration System (Roman Numerals)

  16. Roman Numeration System • If the symbols decrease in value from left to right, then add their values to obtain the value of the Roman numeral as a whole. • If the symbols increase in value from left to right, then subtract the value of the symbol on the left from the symbol on the right to obtain the value of the Roman numeral as a whole.

  17. Examples Write CLXVII as a Hindu-Arabic numeral. Solution: Because the numerals decrease in value from left to right, we add their values to find the value of the Roman numeral as a whole. CLXVII = 100 + 50 + 10 + 5 + 1 + 1 = 167

  18. Write MCMXCVI as a Hindu-Arabic numeral. Solution:

  19. THANK YOU FOR LISTENING!

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