# Truncation

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

## Truncation and floor function

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. This function ist used instead of

for a given number .

## Causes of truncation

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

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

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

## References

## External links

- Wall paper applet that visualizes errors due to finite precision