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Septenary
From Wikipedia, the free encyclopedia
| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic Eastern Arabic Khmer |
Indian family Brahmi Thai |
| East Asian numerals | |
| Chinese Japanese |
Korean |
| Alphabetic numerals | |
| Abjad Armenian Cyrillic Ge'ez |
Hebrew Ionian/Greek Sanskrit |
| Other systems | |
| Attic Etruscan Urnfield Roman |
Babylonian Egyptian Mayan |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 4, 8, 16, 32, 64 | |
| 3, 9, 12, 24, 30, 36, 60, more… | |
The septenary numeral system is the base-7 number system, and uses the digits 0-6.
Fractions expressed in septenary will repeat a sequence of digits unless the denominator is a power of seven. Few fractions can be expressed in a finite number of digits:
| Decimal | Septimal (periodic part) |
| 1/2 | 1/2 = 0.3... |
| 1/3 | 1/3 = 0.2... |
| 1/4 | 1/4 = 0.15... |
| 1/5 | 1/5 = 0.1254... |
| 1/6 | 1/6 = 0.1... |
| 1/7 | 1/10 = 0.1 |
| 1/8 | 1/11 = 0.06... |
| 1/9 | 1/12 = 0.053... |
| 1/10 | 1/13 = 0.0462... |
| 1/12 | 1/15 = 0.04... |
| 1/14 | 1/20 = 0.03... |
| 1/15 | 1/21 = 0.0316... |
| 1/16 | 1/22 = 0.03... |
| 1/18 | 1/24 = 0.025... |
| 1/19 | 1/25 = 0.024... |
| 1/20 | 1/26 = 0.0231... |
| 1/21 | 1/30 = 0.02... |
| 1/24 | 1/33 = 0.02... |
| ... | ... |
| 1/49 | 1/100 = 0.01 |
With the exceptions of the days of the week and the letter nominals of standard Western musical notation, there is no base-7 counting system in general use. However, B. Lukács, of the Hungarian Academy of Sciences Central Research Institute for Physics, believes that linguistic analyses shows that there are lexical remnants in the Uralic group of languages (of which Hungarian and Finnish are members) that is evidence that a septimal system was in use approximately 2500 years ago by the proto-Magyar culture.
The Tau of Sci-fi Table-top battle game Warhammer 40,000 use a base-7 counting system