Number Systems
Number Bases
Base 10
- 10 different symbols for numbers
- Add a new digit after running out of numbers
$$123_{10} = 1\times10^2 + 2\times10^1 + 3\times10^0$$
Base 2
- 2 different symbols for numbers
- Add a new digit after running out of numbers
$$101_2 = 1\times2^2 + 0\times2^1 + 1\times2^0 = 5_{10}$$
Decimal (base 10)
- Most used number base in the world
- 10 fingers
Duodecimal (base 12)
- Advocated by some mathematicians
- Importance
- Twelve sections on the four fingers
- Months of the year
- Units (feet, dozens)
- Chinese zodiac
Vigesimal (base 20)
- Maya numerals
- Aztec numerals
- Yoruba
- Inuit
- French
- Welsh
Heptavigesimal (base 27)
- Oksapmin (language in Papua New Guinea)
Sexagesimal (base 60)
- Babylonian numerals
- Time (minutes, seconds)
Senary (base 6)
- Ndom
Quinary (base 5)
- Gumatj, Ateso, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages
Pentadecimal (base 15)
- Huli
Large Numbers
Long & Short Scale
- Identical up to a million
| Short Scale | Long Scale | |
|---|---|---|
| 10^9 | billion | thousand million / milliard |
| 10^12 | trillion | billion |
| 10^15 | quadrillion | thousand billion / billiard |
| 10^18 | quintillion | trillion |
Short Scale Long Scale Both Other No Data
Chinese Numeral System
- Groups by ten thousands instead of thousands
- Used in China, Japan, Korea, etc
| 1,0000 | 一萬/一万 |
| 10,0000 | 十萬/十万 |
| 100,0000 | 百萬/百万 |
| 1000,0000 | 千萬/千万 |
| 1,0000,0000 | 一億/一亿 |
Indian Numbering System
- Lakh = \(10^5\)
- Crore = \(10^7\)
| 5,00,000 | Five lakh(s) |
| 12,12,12,123 | Twelve crore, twelve lakh, twelve thousand, one hundred and twenty-three |
| 17,00,00,00,000 | One thousand seven hundred crore |
| 6,78,90,00,00,00,000 | Sixty-seven lakh, eighty-nine thousand crore |
Unusual
Number Systems
Body part counting
- Hand/foot = 5
- Man/person = 20
Pirahã
- No number system
-
hói and hoí
- One/two
- Few/many