Truncation

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For other uses, see Truncation (disambiguation).

In mathematics, truncation is the term used for reducing the number of digits right of the decimal point, by discarding the least significant ones.

For example, consider the real numbers

5.6341432543653654

32.438191288

6.3444444444444

To truncate these numbers to 4 decimal digits, we only consider the 4 digits to the right of the decimal point.

The result would be:

5.6341

32.4381

6.3444

Note that in some cases, truncating would yield the same result as rounding, but truncation does not round up or round down the digits; it merely cuts off at the specified digit. The truncation error can be twice the maximum error in rounding.

[edit] Truncation and floor function

Truncation 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

$\mbox{trunc} \left(x,n \right) = \frac{\lfloor 10^n \cdot x \rfloor}{10^n}.$

For negative numbers truncation does not round in the same direction as the floor function: truncation rounds toward zero, the floor function rounds down.