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Relative Error and Significant Digits

Let be an approximation to a real x. The most useful measure of the accuracy of is its absolute error magnitude

and its relative error magnitude

which is undefined, if x = 0. An equivalent definition of relative error magnitude is , where .

Relative error is connected with the notion of correct significant digits or correct significant figures. The significant digits in a number are the first nonzero digit and all succeeding digits.



Dinesh Manocha /Stephen Pizer
Wed Jan 8 00:43:08 EST 1997 / Tue Jan 19 1999