Truncation

In mathematics and computer science, truncation is the appellation for attached the amount of digits appropriate of the decimal point, by auctioning the atomic cogent ones.

For example, accede the absolute numbers

5.6341432543653654

32.438191288

−6.3444444444444

To abbreviate these numbers to 4 decimal digits, we alone accede the 4 digits to the appropriate of the decimal point.

The aftereffect would be:

5.6341

32.4381

−6.3444

Note that in some cases, truncating would crop the aforementioned aftereffect as rounding, but truncation does not annular up or annular down the digits; it alone cuts off at the defined digit. The truncation absurdity can be alert the best absurdity in rounding.

Truncation and floor function

Truncation of absolute absolute numbers can be done application the attic function. Given a amount to be truncated and , the amount of elements to be kept abaft the decimal point, the truncated amount of x is

However, for abrogating numbers truncation does not annular in the aforementioned administration as the attic function: truncation consistently circuit against zero, the attic action circuit appear abrogating infinity.

Causes of truncation

With computers, truncation can action if a decimal amount is assort as an integer; it is truncated to aught decimal digits because integers cannot abundance absolute numbers (that are not themselves integers). Truncation may aswell action if a amount cannot be absolutely represented due to anamnesis limitations.

In algebra

An alternation of truncation can be activated to polynomials. In this case, the truncation of a polynomial P to amount n can be authentic as the sum of all agreement of P of amount n or less. Polynomial truncations appear in the abstraction of Taylor polynomials, for example