1. The Evolution of Numeration Systems
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
Number
Power of 10
Symbol
Name 1
100
Stroke/Staff 10
101
Heel bone
102
Scroll
1,000
103
Lotus Flower
10,000
104
Pointing Finger
100,000
105
Fish/Tadpole
1,000,000
106
Astonished Person

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. The Evolution of Numeration Systems Part II
Section 4.1
The Evolution of Numeration Systems Part II

18. Egyptian Method of Doubling
Power of 2
Value
Times 21 20 1 21 2
= 42 22 4
= 84 23 8
= 168 24 16
= 336 25 32
= 672 26 64
= 1344

19. Example 11: 13 X 43
Doubling Method

20. Example 12: 35 X 21
Doubling Method

21. Roman Numerals Number Roman Numeral 1 I 5 V 10 X 50 L 100 C 500 D
1,000 M
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. The Evolution of Numeration Systems Part III
Section 4.1
The Evolution of Numeration Systems Part III

28. Chinese Number System 1 2 3 4 5 6 7 8 9 10
100
1000

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.