Truncation

In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

Truncation and floor function

Template:Main Truncation of positive real numbers can be done using the floor function. Given a number <math>x \in \mathbb{R}_+</math> to be truncated and <math>n \in \mathbb{N}_0</math>, the number of elements to be kept behind the decimal point, the truncated value of x is

<math>\operatorname{trunc}(x,n) = \frac{\lfloor 10^n \cdot x \rfloor}{10^n}.</math>

However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the <math> \operatorname{floor} </math> function rounds towards negative infinity. For a given number <math>x \in \mathbb{R}_-</math>, the function <math> \operatorname{ceil} </math> is used instead

<math>\operatorname{trunc}(x,n) = \frac{\lceil 10^n \cdot x \rceil}{10^n}</math>.

Causes of truncation

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 algebra

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.<ref>Template:Cite book</ref>

See also

• Arithmetic precision
• Quantization (signal processing)
• Precision (computer science)
• Truncation (statistics)

External links

• Wall paper applet that visualizes errors due to finite precision