From Biocrawler, the free encyclopedia.

A round-off error is the difference between the calculated approximation of a number and its exact mathematical value. Numerical analysis specifically tries to estimate it when using approximation equations and/or algorithms, especially when using finite digits to represent infinite digits of real numbers.

Example

No matter how many digits it has, if the number of digits is finite, the error exists. This kind of error is unavoidable and is named round-off error.

There are, at least, two ways of performing the termination at the limited digit place:

• Chopping: It simply chops off the remaining digits.

0.142857 ≈ 0.142 (chopping at the 5^th digits.)

• Rounding: It adds 5 to the next digit and then chop it. The result may round up or round down.

0.142857 ≈ 0.143 (rounding at the 5^th digits. This is round up   because the next digit, 8, is >= 5)

0.142857 ≈ 0.14   (rounding at the 4^th digits. This is round down because the next digit, 2, is < 5)

See also

Truncation

Wikipedia (http://en.wikipedia.org/wiki/Main_Page) Rounding_error (http://en.wikipedia.org/wiki/Rounding_error) version history (http://en.wikipedia.org/w/index.php?title=Rounding_error&action=history) GNU Free Documentation Lizenz (http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License) CC-by-sa (http://creativecommons.org/licenses/by-sa/2.5/)

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