 |
This article may not meet the general notability guideline. Please help to establish notability by adding reliable, secondary sources about the topic. If notability cannot be established, the article is likely to be merged or deleted. (October 2009) |
| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic Eastern Arabic Indian family |
Khmer Mongolian Thai |
| East Asian numerals | |
| Chinese Counting rods Japanese |
Korean Suzhou |
| Alphabetic numerals | |
| Abjad Armenian Āryabhaṭa Cyrillic |
Ge'ez Greek (Ionian) Hebrew |
| Other systems | |
| Attic Babylonian Brahmi Egyptian Etruscan |
Inuit Mayan Roman Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 4, 8, 16, 32, 64 | |
| 1, 3, 6, 9, 12, 20, 24, 30, 36, 60, more… | |
The base-24 system is a numeral system with 24 as its base.
There are 24 hours in a day, so our time keeping system includes a base-24 component. See also base 12.
Decimal Equivalent
10 twenty four 24 24
100 ? 24^2 = 576
1000 ? 24^3 = 13 824
10 000 ? 24^4 = 331 776
100 000 ? 24^5 = 7 972 624
1 000 000 ? 24^6 = 191 102 976
The digits used for numerals ten (10) to twenty three (23) may be the letters "A" through to "P" ("I" and "O" are skipped to prevent confusion with the digits 1 and 0 in some typefaces).
Fractions
Quadrovigesimal fractions are usually either very simple
1/2 = 0.C 1/3 = 0.8 1/4 = 0.6 1/6 = 0.4 1/8 = 0.3 1/9 = 0.2G 1/C = 0.2 1/G = 0.1C 1/J = 0.18
or complicated
1/5 = 0.4K4K4K4K... recurring (easily rounded to 0.5 or 0.4K) 1/7 = 0.3A6LDH3A6... recurring 1/A = 0.29E9E9E9... recurring (rounded to 0.2A) 1/B = 0.248HAMKF6D248.. recurring (rounded to 0.24) 1/D = 0.1L795CN3GEJB1L7.. recurring (rounded to 0.1L) 1/P = 0.11111... recurring (rounded to 0.11) 1/11 = 0.0P0P0P... recurring (rounded to 0.0P) (1/(5*5))
As explained in recurring decimals, whenever a fraction is written in "decimal" notation, in any base, the fraction can be expressed exactly (terminates) if and only if all the prime factors of its denominator are also prime factors of the base. Thus, in base-10 (= 2×5) system, fractions whose denominators are made up solely of multiples of 2 and 5 terminate: ¹⁄8 = ¹⁄(2*2*2), ¹⁄20 = ¹⁄(2×2×5), and ¹⁄500 (2²×5³) can be expressed exactly as 0.125, 0.05, and 0.002 respectively. ¹⁄3 and ¹⁄7, however, recur (0.333... and 0.142857142857...). In the duodecimal (= 2×2×3) system, ¹⁄8 is exact; ¹⁄20 and ¹⁄500 recur because they include 5 as a factor; ¹⁄3 is exact; and ¹⁄7 recurs, just as it does in base 10.
In practical applications, the nuisance of recurring decimals is encountered less often when quadrovigesimal (or duodecimal) notation is used.
However when recurring fractions do occur in quadrovigesimal notation, they sometimes have a very short period when they are numbers containing one or two factors of five, as 5² = 25 is adjacent to 24. The other adjacent number, 23, is a prime number. So certain powers of five are palindromes in the quadrovigesimal notation:
51 = 5 52 = 11 53 = 55 54 = 121 55 = 5A5 56 = 1331 57 = 5FF5 58 = 14641
The multiples of decimal hundred are 44, 88, CC, GG, LL, 110, etc.
Natural languages
Umbu-Ungu, also known as Kakoli, is reported to have base-24 numerals.[1][2] Tokapu means 24, tokapu talu means 24×2 = 48, and tokapu tokapu means 24×24 = 576.
References
- ^ Gordon, Raymond G., Jr., ed. (2005), "Umbu-Ungu", Ethnologue: Languages of the World (15 ed.), http://www.ethnologue.com/show_language.asp?code=ubu, retrieved 2008-03-16
- ^ Bowers, Nancy; Lepi, Pundia (1975), "Kaugel Valley systems of reckoning", Journal of the Polynesian Society 84 (3): 309–324, http://www.ethnomath.org/resources/bowers-lepi1975.pdf
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
