mod 1

The fractional part or decimal part of a non‐negative real number



x


{\displaystyle x}
is the excess beyond that number's integer part. If the latter is defined as the largest integer not greater than x, called floor of x or



⌊
x
⌋


{\displaystyle \lfloor x\rfloor }
, its fractional part can be written as:




frac
⁡
(
x
)
=
x
−
⌊
x
⌋
,

x
>
0


{\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).

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