# Fractional part

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 $x-\lfloor x\rfloor$, 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 $0 \le p < q$; hence, the fractional part will always be less than 1. For example, if x = 1.05, then the fractional part of x is .05 and can be expressed as 5/100 = 1/20.

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