Truncation

For other uses, see Truncation (disambiguation).

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

Truncation and floor function

Main article: Floor and ceiling functions

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

\operatorname {trunc} (x,n)={\frac {\lfloor 10^{n}\cdot x\rfloor }{10^{n}}}.

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

\operatorname {trunc} (x,n)={\frac {\lceil 10^{n}\cdot x\rceil }{10^{n}}}

for a given number $x\in \mathbb {R} _{-}$ .

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]

References

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

External links

Wall paper applet that visualizes errors due to finite precision

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