High Quality Content by WIKIPEDIA articles! In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth order approximation, a first order approximation, a second order approximation, and so forth. Formally, an nth order approximation is one where the order of magnitude of the error is at most n; in terms of big O notation, with error bounded by O(xn). In suitable circumstances, approximating a function by a Taylor polynomial of degree n yields an nth order approximation, by Taylor's theorem: a first order approximation is a linear approximation, and so forth.

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