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