Fract

Fract, short for fractional part, is a mathematical concept used to describe the non-integer portion of a real number. In many programming and mathematical contexts, fract(x) denotes the fractional part of x, separating it from its integer part. It is distinct from the broader idea of a fraction and from fractals, which are geometric shapes.

The standard mathematical definition of fract(x) is x minus the floor of x. That is fract(x) = x − floor(x). The floor function returns the greatest integer less than or equal to x. With this convention, fract(x) lies in the interval [0, 1). For example, fract(3.75) = 0.75 and fract(−2.7) = 0.3. The function is periodic with period 1, since fract(x + 1) = fract(x).

There are alternative conventions used in some contexts. Some definitions use x minus the truncation of x, where trunc(x) removes the fractional part toward zero. In that case fract(−2.7) would be −0.7. Because of these variations, the term fractional part can refer to slightly different concepts depending on the convention in use.

In computing, fract can be implemented via various methods, such as fmod(x, 1.0) or by computing x − floor(x). Some languages also provide dedicated functions (for example, modf in C) that return both the integer and fractional parts separately. The choice of convention affects the sign and interpretation of the result.

Applications of fract appear in numeric algorithms, computer graphics, signal processing, and anywhere a value must be scaled to a unit interval or repeated cyclically. See also fractional part, modulo, floor function, and truncation.