In Mathematical, the truncation is a term used to cut the decimal Développement of a Nombre to a certain number of figures after the comma, or the Développement limited of a function to a certain order.

Truncation of a number

For example, let us consider the real numbers:

5,6341432543653654

32,438191288

6,3444444444444

For to truncate these numbers with four decimal, only are kept the four figures after the comma.

The result would be:

5,6341

32,4381

6,3444

Let us notice that in certain cases, truncation gives the same result as a Arrondi, but does not correspond to a rounding by excess or defect; it cuts out simply the decimals with a precise position. The Erreur of truncation cannot twice exceed the maximum error of a round-off.

Truncation and whole left function

Truncation can be carried out by using the whole function left. Either $x\; \backslash \; in\; \backslash \; mathbb\; \{R\}\; \_+$ a number to be truncated and $n\; \backslash \; in\; \backslash \; mathbb\; \{NR\}\; ^\; \{*\}$, the number of figures to be kept after the comma, the decimal truncation of $x$ with $n$ is equal to:

$\backslash \; frac\; \{\backslash \; left\; 10^n\; \backslash \; cdot\; X\; \backslash \; right\}\; \{10^n\},$

where $$ indicates the whole part of $a$.

See too

• arithmetic Precision
• whole Function left

Truncation of a limited development

External bonds

• Applette wallpaper

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