# Dictionary Definition

truncation

### Noun

1 the property of being truncated or short [syn:
shortness]

2 the replacement of an edge or solid angle (as
in cutting a gemstone) by a plane (especially by a plane that is
equally inclined to the adjacent faces)

3 the act of cutting short; "it is an obvious
truncation of the verse"; "they were sentenced to a truncation of
their limbs"

# User Contributed Dictionary

## English

### Noun

- The act of truncating or shortening (in all senses)
- The removal of the least significant digits from a decimal number
- The replacement of a solid angle by a plane (or a similar operation in other dimensions)

# Extensive Definition

In mathematics, truncation is
the term for limiting 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.

In statistics, the term
truncation is used differently and can be thought of in the same
context as censoring.
Usually the values that insurance adjusters receive are either left
truncated, right censored or both. For example, if policyholders
are subject to a policy limit, u, then and loss amounts that are
actually above u are reported to the insurance company as being
exactly u because u is the amount the insurance companies pay. The
insurance company knows that the actual loss is greater than u but
they don't know what is is. On the other hand, left truncation
occurs when policyholders are subject to a deductible. If
policyholders are subject to a deductible, d, any loss amount that
is less than d will not even be reported to the insurance company.
Any loss amount that is greater than d will be reported to the
insurance company is loss - d because that is the amount the
insurance company has to pay. Therefore insurance loss data is left
truncated because the insurance company doesn't know if there are
values below a specific amount. They don't know how many losses
occur or how much each loss is.

## Truncation and floor function

Truncation can be done using the floor function. Given a number x \in \mathbb_+ to be truncated and n \in \mathbb_0, the number of elements to be kept behind the decimal point, the truncated value of x is- \mbox \left(x,n \right) = \frac.

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

## See also

- Precision (arithmetic)
- Floor function
- Asterisks (*), used on truncation

## External links

truncation in Catalan: Truncament

truncation in Spanish: Truncamiento

truncation in Korean: 버림

truncation in Italian: Troncamento

truncation in Japanese: 端数処理

truncation in Sicilian: Truncamentu

truncation in Swedish:
Trunkering