It also is used when a number is not rational, such as the number π, which often is shortened to 3.14159, or 1.414 as the shortened form of √ 2. However some known form may exist and may be able to represent the real form so that no significant deviation can be found. Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain. Diophantine approximation deals with approximations of real numbers by rational numbers. The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation.Īpproximation theory is a branch of mathematics, a quantitative part of functional analysis. Approximations might also be used if incomplete information prevents use of exact representations. An approximate model is used to make calculations easier. In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct similar, but not exactly the same (e.g., the approximate time was 10 o'clock).Īlthough approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In everyday English, words such as roughly or around are used with a similar meaning. Words like approximate, approximately and approximation are used especially in technical or scientific contexts.
The word approximation is derived from Latin approximatus, from proximus meaning very near and the prefix ad- ( ad- before p becomes ap- by assimilation) meaning to.
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