Rounding - Revision history

Karl Jones at 02:48, 26 April 2016

2016-04-26T02:48:03Z

Karl Jones: /* See also */

2016-03-01T00:52:53Z

‎See also

Karl Jones at 15:25, 5 February 2016

2016-02-05T15:25:34Z

Karl Jones: /* See also */

2015-09-13T11:45:10Z

‎See also

Karl Jones: Created page with "'''Rounding''' a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example,..."

2015-09-13T11:44:56Z

Created page with "'''Rounding''' a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example,..."

New page

'''Rounding''' a [[numerical value]] means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.

(TO DO: expand, organize, cross-reference, illustrate.)

== Description ==

Rounding is often done to obtain a value that is easier to [[report]] and [[communicate]] than the original. Rounding can also be important to avoid [[overprecision|misleadingly precise]] reporting of a computed number, [[measurement]] or [[estimate]]; for example, a quantity that was computed as 123,456 but is known to be [[Accuracy and precision|accurate]] only to within a few hundred units is better stated as "about 123,500."

On the other hand, rounding of exact numbers will introduce some [[round-off error]] in the reported result. Rounding is almost unavoidable when reporting many computations — especially when dividing two numbers in [[integer]] or [[fixed-point arithmetic]]; when computing mathematical functions such as [[square root]]s, [[logarithm]]s, and [[sine]]s; or when using a [[floating point]] representation with a fixed number of [[significant digit]]s. In a sequence of calculations, these rounding errors generally accumulate, and in certain [[ill-conditioned]] cases they may make the result meaningless.

Accurate rounding of [[transcendental function|transcendental mathematical functions]] is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as "the table-maker's dilemma".

== Quantization (signal processing) ==

Rounding has many similarities to the [[quantization (signal processing)|quantization]] that occurs when [[physical quantity|physical quantities]] must be encoded by numbers or [[digital signal]]s.

A wavy [[equals sign]] (<big>'''[[≈]]'''</big>) is sometimes used to indicate rounding of exact numbers. For example: 9.98 ≈ 10.

== See also ==

* [[Mathematics]]
* [[Quantization (signal processing)]]
* [[Round-off_error]]

== External links ==

* [https://en.wikipedia.org/wiki/Rounding Rounding] @ Wikipedia

← Older revision		Revision as of 15:25, 5 February 2016
Line 1:		Line 1:
	'''Rounding''' a [[numerical value]] means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.		'''Rounding''' a [[numerical value]] means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.
−
−	~~(TO DO: expand, organize, cross-reference, illustrate.)~~

	== Description ==		== Description ==

@@ Line 1: / Line 1: @@
-'''Rounding''' a [[numerical value]] means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.
+In [[mathematics]], '''rounding''' a [[numerical value]] means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.
 == Description ==
@@ Line 27: / Line 27: @@
 * [https://en.wikipedia.org/wiki/Rounding Rounding] @ Wikipedia

@@ Line 17: / Line 17: @@
 == See also ==
 * [[Mathematics]]
 * [[Quantization (signal processing)]]
 * [[Round-off error]]