In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

Truncation of positive real numbers can be done using the floor function. Given a number ${\displaystyle x\in \mathbb {R} _{+}}$ to be truncated and ${\displaystyle n\in \mathbb {N} _{0}}$, the number of elements to be kept behind the decimal point, the truncated value of x is

However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the ${\displaystyle \operatorname {floor} }$ function rounds towards negative infinity. For a given number ${\displaystyle x\in \mathbb {R} _{-}}$, the function ${\displaystyle \operatorname {ceil} }$ is used instead

With computers, truncation can occur when a decimal number is typecast as an integer; it is truncated to zero decimal digits because integers cannot store non-integer real numbers.

An analogue of truncation can be applied to polynomials. In this case, the truncation of a polynomial P to degree n can be defined as the sum of all terms of P of degree n or less. Polynomial truncations arise in the study of Taylor polynomials, for example.