Troncamento (matematica)

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Il troncamento è l'operazione che approssima la rappresentazione di un numero limitando il numero di cifre utilizzabili per tale rappresentazione.

Dato un intero x in base $\beta$ , secondo il teorema di rappresentazione in base, lo possiamo rappresentare come:

x=\operatorname {sgn} (x)m\beta ^{p},

dove la mantissa m è:

m=\sum _{i=1}^{\infty }c_{i}\beta ^{-i}.

In caso di troncamento il numero di cifre $c_{i}$ utilizzabili è limitato, quindi l'estremo superiore della sommatoria non sarà più $\infty$ ma un intero $t>0$ . A questo punto il numero x è rappresentato come:

x=\operatorname {sgn} (x)\beta ^{p}\sum _{i=1}^{t}c_{i}\beta ^{-i}.

Ad esempio, data la base $\beta =10$ e $t=4$ :

\alpha =16,7345

diventa 16,73;

\alpha =23,9999

diventa 23,99.

Come abbiamo visto tra il numero reale e quello troncato ci sono delle differenze, ossia abbiamo introdotto un errore di troncamento.

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