# Fractional part

All real numbers can be written in the form n + r where n is an integer (the integer part) and the remaining fractional part r is a nonnegative real number less than one. For a positive number written in decimal notation, the fractional part corresponds to the digits appearing after the decimal point.

The fractional part of a real number x is ${\displaystyle x-\lfloor x\rfloor }$, where ${\displaystyle \lfloor \;\rfloor }$ is the floor function. It is sometimes denoted ${\displaystyle \{x\},\langle x\rangle }$ or ${\displaystyle x\,{\bmod {\,}}1}$.

If x is rational, then the fractional part of x can be expressed in the form ${\displaystyle p/q}$, where p and q are integers and ${\displaystyle 0\leq p. For example, if ${\displaystyle x=1.05}$, 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 ${\displaystyle x-\lfloor x\rfloor }$ Template:Harv or as the part of the number to the right of the radix point Template:Harv. 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.