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# Octal

The octal numeral system is the base 8 number system, and uses the digits 0-7.

Octal numerals can be made from binary numerals by grouping consecutive digits into 3s (from right).

E.g The binary for 74 is 1001010, which groups into 1 001 010. So the octal is 112.

Octal is sometimes used in computing instead of hexadecimal. It has the advantage of not requiring any extra symbols as digits.

Octal counting may have been used in the past instead of decimal counting, by counting either the gaps between fingers or the non-thumb fingers. This may explain why the Latin for nine novem is so much like the Latin for new novus. It may have meant new number.

## Fractions

Octal is as good as binary and hexadecimal for fractions, since the only prime factors for their bases are 2.

 Fraction Octal Octal expansion 1/2 1/2 0.4 1/3 1/3 0.25252525 recurring 1/4 1/4 0.2 1/5 1/5 0.14631463 recurring 1/6 1/6 0.125252525 recurring 1/7 1/7 0.111111 recurring 1/8 1/10 0.1 1/9 1/11 0.07070707 recurring 1/10 1/12 0.063146314 recurring