Base 5

Quinary (base-5) is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. The base five is stated from 0–4.

In the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220.

As five is a prime number, only the reciprocals of the powers of five terminate, although its location between two highly composite numbers (4 and 6) guarantees that many recurring fractions have relatively short periods.

Today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a sub-base system, is sexagesimal, base 60, which used 10 as a sub-base.

Each quinary digit has log₂5 (approx. 2.32) bits of information.

Many languages use quinary number systems, including Gumatj, Nunggubuyu,Kuurn Kopan Noot,Luiseño and Saraveca. Gumatj is a true "5–25" language, in which 25 is the higher group of 5. The Gumatj numerals are shown below:

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