# 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 , where is the floor function. It is sometimes denoted or .

If *x* is rational, then the fractional part of *x* can be expressed in the form , where *p* and *q* are integers and . For example, if , 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 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.

## 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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