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In [[mathematics]] and [[computer science]], '''truncation''' is the term for limiting the number of [[numerical digit|digit]]s right of the [[decimal point]], by discarding the least significant ones. | |||
[ | For example, consider the [[real number]]s | ||
: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 [[Approximation error|error]] can be twice the maximum error in rounding. | |||
== Truncation and floor function == | |||
{{main|Floor and ceiling functions}} | |||
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 floor function rounds towards negative infinity. | |||
== Causes of truncation == | |||
With computers, truncation can occur when a decimal number is [[type conversion|typecast]] as an [[integer]]; it is truncated to zero decimal digits because integers cannot store [[real numbers]] (that are not themselves integers). | |||
== In algebra == | |||
An analogue of truncation can be applied to [[polynomial]]s. 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 polynomial]]s, for example.<ref>{{cite book|first=Michael|last=Spivak|title=Calculus|edition=4th|year=2008|isbn=978-0-914098-91-1|page=434}}</ref> | |||
== See also == | |||
* [[Arithmetic precision]] | |||
* [[Floor function]] | |||
* [[Quantization (signal processing)]] | |||
* [[Precision (computer science)]] | |||
* [[Truncation (statistics)]] | |||
== References == | |||
{{Reflist}} | |||
== External links == | |||
* [http://to-campos.planetaclix.pt/fractal/walle.html Wall paper applet] that visualizes errors due to finite precision | |||
[[Category:Numerical analysis]] | |||
[[ja:端数処理]] | |||
Revision as of 12:03, 7 November 2013
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I'm learning Norwegian literature at a local college and I'm just about to graduate.
I have a part time job in a the office.
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In mathematics and computer science, 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.
Truncation and floor function
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Truncation of positive real numbers can be done using the floor function. Given a number to be truncated and , the number of elements to be kept behind the decimal point, the truncated value of x is
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.
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 real numbers (that are not themselves integers).
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.[1]
See also
- Arithmetic precision
- Floor function
- Quantization (signal processing)
- Precision (computer science)
- Truncation (statistics)
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
External links
- Wall paper applet that visualizes errors due to finite precision
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534