# Truncation

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

## Truncation and floor function[edit]

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 ceil is used instead

- .

In some cases trunc(*x*,0) is written as [*x*].^{[citation needed]} See Notation of floor and ceiling functions.

## Causes of truncation[edit]

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 algebra[edit]

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 also[edit]

- Arithmetic precision
- Quantization (signal processing)
- Precision (computer science)
- Truncation (statistics)

## References[edit]

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

## External links[edit]

- Wall paper applet that visualizes errors due to finite precision