Truncation

In

.

Truncation and floor function

Truncation of positive real numbers can be done using the

. Given a number ${\displaystyle x\in \mathbb {R} _{+}}$ to be truncated and ${\displaystyle n\in \mathbb {N} _{0}}$, the number of elements to be kept behind the decimal point, the truncated value of x is

${\displaystyle \operatorname {trunc} (x,n)={\frac {\lfloor 10^{n}\cdot x\rfloor }{10^{n}}}.}$

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

${\displaystyle \operatorname {trunc} (x,n)={\frac {\lceil 10^{n}\cdot x\rceil }{10^{n}}}}$.

In some cases trunc(x,0) is written as [x].^{[citation needed]} See Notation of floor and ceiling functions.

Causes of truncation

With computers, truncation can occur when a decimal number is

.

In algebra

An analogue of truncation can be applied to

See also

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

References

External links

• Wall paper applet that visualizes errors due to finite precision