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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[edit]

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.

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 real numbers (that are not themselves integers).

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]


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

External links[edit]