The Accuracy of Computation with Approximate Numbers
1. General Considerations. The number of figures necessarily free from error in the result of a piece of computation may be determined by studying the relation between the number of digits in the result and the number of digits in the maximum error of the computation. It is the purpose of this essay to derive rules for the determination of the, number of digits which are certain to be correct in computations based on measurement, but it must be understood that these rules state the minimum number of correct digits so that the resuk of a specific piece of computation may be accurate for more places than the rules indicate. 2. Notation. Since the location of the decimal point has no connection with significant figures in a given number, it is assumed that the decimal point follows the last significant figure in each of the original numbers, the argument being somewhat simplified by this assumption. Accordingly the greatest error in the statement of the original numbers is ? 0.5. Let / and .B be the true values of two numbers such that A tQ /Oand B5i . , where m and n are positive incegers and where 0.1 < a < 1.0 and where 0.1 & < 1.0. Then by the convention adopted above, the number of significant figures in A and B are m and no respectively, and the observed values are not less than A 0.5 and B0.5 and not more than