1. 4.4 Looking Back at Early Numeration Systems

2. The Egyptian Numeration System
The Egyptians used the oldest numeration system called hieroglyphic notation.

3. The Roman Numeration System
Roman Numeral I V X L C D M
Hindu-Arabic Numeral 1 5 10 50
100
500
1000
The Roman numerals were used until the eighteenth century and are still commonly used today for outlining, on clocks, and in numbering some pages in books.

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, , ,
= 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 = =
Now use the table to find the Egyptian symbol that matches each quantity. Thus, 1752 can be expressed as

6. The Roman Numeration System
Roman Numeral I V X L C D M
Hindu-Arabic Numeral 1 5 10 50
100
500
1000
Used until the eighteenth century
Still commonly used today for outlining, on clocks, and in numbering some pages in books
Super Bowl numbering

7. The 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.

8. Example 3: Using Roman Numerals
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 = = 167

9. Example 4: Using Roman Numerals
Write MCMXCVI as a Hindu-Arabic numeral.
Solution:

10. Your Turn Write the following Roman numerals in Hindu-Arabic numerals.
MMCXVI
= = 2116
MCMDXII
= = 2412
MDCCIXIII
= = 1712

11. The Traditional Chinese Numeration System

12. Using the Traditional Chinese Numeration System
Write 3264 as a Chinese numeral.

13. The Traditional Japanese Numeration一 二 三 四 五 六 七 八 九 十 百 千 万
Hindu-Arabic 1 2 3 4 5 6 7 8 9 10
100
1,000
10,000 (104)
Traditional Japanese
億 (oku)
兆 (chou)
京 (kei)
Hindu-Arabic
100,000,000 (108)
1,000,000,000,000 (1012)
10 (1016)
E.g.,
World population: = 72億 Honda Civic Hybrid: ¥2,500,000 = ¥250万 ≈ $25,000

14. Japanese Currency
¥1000
¥5000
¥10,000 ¥1
¥10
¥50

15. Unit Prefix 1,000 103 kilo- 1,000,000 106 mega-
1,000,000, giga-
1,000,000,000, tera-
1,000,000,000,000, peta-
1,000,000,000,000,000, exa-

16. Unit Prefix 0.1 10-1 deci- 0.01 10-2 centi- 0.001 10-3 milli-
micro-
nano-
pico-

17. The Ionic Greek Numeration System
The ancient Greeks used letters from their alphabet for numerals. The symbols are written right next to one another.

18. 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 = = 734
Thus, ψλδ represents 734 in Hindu-Arabic numerals.