AskDefine | Define truncate

Dictionary Definition

truncate adj : terminating abruptly by having or as if having an end or point cut off; "a truncate leaf"; "truncated volcanic mountains"; "a truncated pyramid" [syn: truncated]


1 replace a corner by a plane
2 approximate by ignoring all terms beyond a chosen one; "truncate a series"
3 make shorter as if by cutting off; "truncate a word"; "Erosion has truncated the ridges of the mountains" [syn: cut short]

User Contributed Dictionary



  1. To shorten something as if by cutting off part of it.
  2. To shorten a decimal number by removing trailing (or leading) digits; to chop.
  3. To replace a corner by a plane (or to make a similar change to a crystal).

Derived terms



shorten something as if by cutting off part of it
shorten a decimal number by removing trailing (or leading) digits; to chop
  • Dutch: afronden naar beneden
replace a corner by a plane


  1. truncated
  2. In the context of "botany|anatomy": Having an abrupt termination.


botany, anatomy: having an abrupt termination

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
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:
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

External links

truncate in Catalan: Truncament
truncate in Spanish: Truncamiento
truncate in Korean: 버림
truncate in Italian: Troncamento
truncate in Japanese: 端数処理
truncate in Sicilian: Truncamentu
truncate in Swedish: Trunkering

Synonyms, Antonyms and Related Words

abbreviate, abridge, abscind, abstract, amputate, annihilate, ban, bar, blemish, bob, boil down, capsulize, clip, compress, condense, contract, crop, cull, curtail, cut, cut away, cut back, cut down, cut off, cut off short, cut out, cut short, deface, deform, disfigure, disproportion, dock, elide, eliminate, enucleate, epitomize, eradicate, except, excise, exclude, extinguish, extirpate, foreshorten, isolate, knock off, lop, mar, misshape, mow, mutilate, nip, pare, peel, pick out, poll, pollard, prune, reap, recap, recapitulate, reduce, retrench, root out, rule out, set apart, set aside, shave, shear, shorten, snub, stamp out, strike off, strip, strip off, stunt, sum up, summarize, synopsize, take in, take off, take out, telescope, top, trim, wipe out
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