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.

Truncation and floor function

Truncation can be done using the floor function. Given a number x in mathbb{R}_+ to be truncated and n in mathbb{N}_0, the number of elements to be kept behind the decimal point, the truncated value of x is:mbox{trunc} left(x,n ight) = frac{lfloor 10^n cdot x floor}{10^n}.

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

* Floor function
* Precision (arithmetic)
* Truncation (statistics)

External links

* [ Wall paper applet]

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Look at other dictionaries:

  • Truncation — Trun*ca tion, n. [L. truncatio.] 1. The act of truncating, lopping, or cutting off. [1913 Webster] 2. The state of being truncated. [1913 Webster] 3. (Min.) The replacement of an edge or solid angle by a plane, especially when the plane is… …   The Collaborative International Dictionary of English

  • truncation — 1570s, from L.L. truncationem, noun of action from truncare (see TRUNCATE (Cf. truncate)) …   Etymology dictionary

  • truncation — noun 1. the property of being truncated or short • Syn: ↑shortness • Derivationally related forms: ↑short (for: ↑shortness) • Hypernyms: ↑lowness 2 …   Useful english dictionary

  • truncation — /trung kay sheuhn/, n. 1. the act or process of truncating. 2. the quality or state of being truncated. 3. Pros. the omission of one or more unaccented syllables at the beginning or the end of a line of verse. 4. Banking. a system of electronic… …   Universalium

  • truncation — atmetimas statusas T sritis informatika apibrėžtis Operacija arba funkcija skaičiaus trupmeninei daliai sutrumpinti atmetant tam tikrą jo skilčių skaičių. Pavyzdžiui, skaičiai 3,000001 ir 3,999999 po visų trupmeninių skilčių atmetimo tampa lygūs… …   Enciklopedinis kompiuterijos žodynas

  • truncation — truncate ► VERB ▪ shorten by cutting off the top or the end. DERIVATIVES truncation noun. ORIGIN Latin truncare maim …   English terms dictionary

  • truncation — noun see truncate II …   New Collegiate Dictionary

  • truncation — noun a) The act of truncating or shortening (in all senses) b) The removal of the least significant digits from a decimal number See Also: truncate …   Wiktionary

  • truncation —    A horizontal or vertical clean cut through a topographic feature [16] …   Lexicon of Cave and Karst Terminology

  • truncation — trun·ca·tion || trʌŋ keɪʃn n. act of shortening, act of cutting short; quality of being truncated; leaving out of unaccented syllables at the beginning or end of a line (Literature) …   English contemporary dictionary

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