View source for Round-off error

In [[mathematics]], a '''round-off error''', also called '''rounding error''', is the difference between the calculated [[approximation]] of a number and its exact mathematical value due to [[rounding]].

== Description ==

Round-off error is a form of [[quantization error]].

One of the goals of [[numerical analysis]] is to [[error analysis (mathematics)|estimate]] errors in calculations, including round-off error, when using approximation [[equation]]s and/or [[algorithm]]s, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits).

When a sequence of calculations subject to rounding error is made, errors may accumulate, sometimes dominating the calculation. In [[ill-conditioned]] problems, significant error may accumulate.

== Representation error ==

The error introduced by attempting to represent a number using a finite string of digits is a form of round-off error called ''representation error''.

== See also ==

* [[Algorithm]]
* [[Approximation]]
* [[Computer science]]
* [[Error analysis (mathematics)]]
* [[Mathematics]]
* [[Numerical analysis]]
* [[Numerical stability]]
* [[Rounding]]

== External links == 

* [https://en.wikipedia.org/wiki/Round-off_error Round-off error] @ Wikipedia

[[Category:Mathematics]]
[[Category:Numbers]]