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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


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

External linksEdit