# Fractional part

The fractional part of a real number x is $x-\lfloor x\rfloor$, where $\lfloor\;\rfloor$ is the floor function. It is sometimes denoted $\{x\}, \langle x \rangle$ or $x\,\bmod\,1$.
If x is rational, then the fractional part of x can be expressed in the form $p / q$, where p and q are integers and $0 \le p < q$. For example, if $x = 1.05$, then the fractional part of x is .05 and can be expressed as 5/100 = 1/20.
The fractional part of negative numbers does not have a universal definition. It is either defined as $x-\lfloor x\rfloor$ (Graham, Knuth & Patashnik 1992) or as the part of the number to the right of the radix point (Daintith 2004). For example, the number -1.3 has a fractional part of 0.7 according to the first definition and 0.3 according to the second definition.