# Truncation

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

## Truncation and floor functionEdit

Truncation of positive real numbers can be done using the floor function. Given a number to be truncated and , 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 floor function rounds towards negative infinity. For a given number , the function

is used instead.

## Causes of truncationEdit

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.

## In algebraEdit

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.^{[1]}

## See alsoEdit

## ReferencesEdit

**^**Spivak, Michael (2008).*Calculus*(4th ed.). p. 434. ISBN 978-0-914098-91-1.

## External linksEdit

- Wall paper applet that visualizes errors due to finite precision