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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 $0\leq p<q$. For example, if $x=1.05$, then the fractional part of x is .05 and can be expressed as 5/100 = 1/20.

See also

• Floor and ceiling functions, the main article on fractional parts
• Equidistributed sequence
• One-parameter group
• Pisot–Vijayaraghavan number
• Significand

References

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