Septenary

The septenary numeral system is the base seven number system, and uses the digits 0-6.

Septenary is a very good numeral system for repeating fractions, but poor for terminating fractions.

Decimal  Septimal
1/2      1/2 = 0.33333....
1/3      1/3 = 0.22222....
1/4      1/4 = 0.151515....
1/5      1/5 = 0.125412541254....
1/6      1/6 = 0.11111....
1/7      1/10 = 0.1
1/8      1/11 = 0.060606....
1/9      1/12 = 0.053053053...
1/10     1/13 = 0.046204620462....
1/12     1/15 = 0.04040404....
1/14     1/20 = 0.0333333...
1/15     1/21 = 0.031603160316....
1/16     1/22 = 0.0303030...
1/18     1/24 = 0.025025025...
1/19     1/25 = 0.024024024...
1/20     1/26 = 0.023102310231...
1/21     1/30 = 0.0222222...
1/24     1/33 = 0.02020202....

With the exception of the days of the week, 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.

See also

THE GREAT 7 by B. Lukács