Round-off error

From Wikipedia, the free encyclopedia

(Redirected from Rounding error)
Jump to: navigation, search

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

Notation Represent Approximate Error
1/7 0.142 857 0.142 857 1/7 000 000
ln 2 0.693 147 180 559 945 309 41...   0.693 147 0.000 000 180 559 945 309 41...
log10 2 0.301 029 995 663 981 195 21...   0.3010 0.000 029 995 663 981 195 21...
∛ 2  1.259 921 049 894 873 164 76...   1.25992 0.000 001 049 894 873 164 76...
√ 2  1.414 213 562 373 095 048 80...   1.41421 0.000 003 562 373 095 048 80...
e 2.718 281 828 459 045 235 36...   2.718 281 828 459 045   0.000 000 000 000 000 235 36...
π 3.141 592 653 589 793 238 46...   3.141 592 653 589 793 0.000 000 000 000 000 238 46...

Increasing the number of digits allowed in a representation reduces the magnitude of possible roundoff errors, but any representation limited to finitely many digits will still cause some degree of roundoff error for uncountably many real numbers. This kind of error is unavoidable for conventional representations of numbers.

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

  • truncation: simply chop off the remaining digits.
0.142857 ≈ 0.142 (chopping at the 5th digits.)
  • rounding: add 5 to the next digit and then chop it. The result may round up or round down.
0.142857 ≈ 0.143 (rounding at the 5th digits. This is rounded up because the next digit, 8\ge5)
0.142857 ≈ 0.14 (rounding at the 4th digits. This is rounded down because the next digit, 2 < 5 \!\ )

This mathematical analysis-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org/wiki/Round-off_error"
Advanced Search
Included Web Search Engines


Safe Search

close

Top Matching Results

Occasionally Search.com will highlight specialized results that are based on the context of your query. Examples of specialized results include specific links to news, images, or video.

Top Matching Results may highlight information from other Search.com pages, content from the CNET Network of sites, or third party content. The listings are based purely on relevance. Search.com does not receive payment for listings in this section but our partners that provide this data may get paid for listing these products.

Sponsored Links

This section contains paid listings which have been purchased by companies that want to have their sites appear for specific search terms and related content. These listings are administered, sorted and maintained by a third party and are not endorsed by Search.com.

Search Results

Search.com sends your search query to several search engines at one time and integrates the results into one list which has been sorted by relevance using Search.com's proprietary algorithm. You can customize the list of search engines included in your metasearch from the preferences.

The search engines that are used in your metasearch may allow companies to pay to have their Web sites included within the results. To view the Paid Inclusion policy for a specific search engine, please visit their Web site. Search.com does not accept payment or share revenue with any search engine partner for listings in this section.