Fractional part

The fractional part or decimal part of a non‐negative real number ${\displaystyle x}$ is the excess beyond that number's integer part. The latter is defined as the largest integer not greater than x, called floor of x or ${\displaystyle \lfloor x\rfloor }$. Then, the fractional part can be formulated as a difference:

${\displaystyle \operatorname {frac} (x)=x-\lfloor x\rfloor ,\;x>0}$.

For a positive number written in a conventional positional numeral system (such as binary or decimal), its fractional part hence corresponds to the digits appearing after the radix point. The result is a real number in the half-open interval [0, 1).