Fractional part

The fractional part or decimal part^[1] 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:

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

The fractional part of logarithms,^[2] specifically, is also known as the mantissa; by contrast with the mantissa, the integral part of a logarithm is called its characteristic.^[3][4] The word mantissa was introduced by Henry Briggs.^[5]

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, such as the decimal point in English. The result is a real number in the half-open interval [0, 1).