Septenary
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| 2, 4, 8, 16, 32, 64 | |
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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 |
The times tables in base 7:
| - | 1 | 2 | 3 | 4 | 5 | 6 | 10 |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 10 |
| 2 | 2 | 4 | 6 | 11 | 13 | 15 | 20 |
| 3 | 3 | 6 | 12 | 15 | 21 | 24 | 30 |
| 4 | 4 | 11 | 15 | 22 | 26 | 33 | 40 |
| 5 | 5 | 13 | 21 | 26 | 34 | 42 | 50 |
| 6 | 6 | 15 | 24 | 33 | 42 | 51 | 60 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 100 |
Also in base 7: π = 3.0663651432... e = 2.5012410654...
One advantage of this system is that 3.1 (22/7) is a reasonably good approximation for Pi.
[edit] In Fiction
- The Tau of Sci-fi Table-top battle game Warhammer 40,000 use a base-7 counting system.
- In the TV series Doctor Who the time lords employ a number system using base 7.
- The Halo 3 Alternate Reality Game "IRIS" used a countdown clock in base-7.
