Related Searches
Definitions

# Septenary

[sep-tuh-ner-ee]
The septenary numeral system is the base-7 number system, and uses the digits 0-6.

## Multiplication table

1 2 3 4 5 6 10
2 4 6 11 13 15 20
3 6 12 15 21 24 30
4 11 15 22 26 33 40
5 13 21 26 34 42 50
6 15 24 33 42 51 60
10 20 30 40 50 60 100

## Fractions

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

## Irrational Numbers

 Algebraic irrational number Transcendental irrational number In decimal In septenary √2 (the length of the diagonal of a unit square) 1.41421356237309... (≈ 1.414) 1.262034545211232611 ... (≈ 1.262) √3 (the length of the diagonal of a unit cube, or twice the height of an equilateral triangle of unit side) 1.73205080756887... (≈ 1.732) 1.506044021410166456 ... (≈ 1.506 ≈ 1.5) √5 (the length of the diagonal of a 1×2 rectangle) 2.2360679774997... (≈ 2.236) 2.143654106250351 ... (≈ 2.144) φ (phi, the golden ratio = ) 1.6180339887498... (≈ 1.618) 1.42166203646016... (≈ 1.422) In decimal In septenary π (pi, the ratio of circumference to diameter) 3.1415926535898... (≈ 3.1416) 3.06636514320361341... (≈ 3.1) e (the base of the natural logarithm) 2.718281828459045... (≈ 2.718) 2.50124106542265... (≈ 2.5)

One advantage of this system is that 3.1 (22/7) is a reasonably good approximation for Pi.

## 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.
Search another word or see septenaryon Dictionary | Thesaurus |Spanish