CHINESE JOURNAL OF PHYSICS VOL. 38, NO. 1 FEBRUARY 2000

On the Standard Rounding Rule for Addition and Subtraction

Wei Lee¹, Christopher L. Mulliss², and Hung-Chih Chiu<sup>1

1</sup>Department of Physics, Chung Yuan Christian University,

Chung-Li, Taiwan 320, R.O.C.
²Department of Physics and Astronomy, University of Toledo,

Toledo, Ohio 43606, U.S.A.
(Received June 27, 1999)

An investigation of the commonly suggested rounding rule for addition and subtraction is presented including its derivation from a basic assumption. Through theoretical study and Monte-Carlo simulations, it is shown that this rule predicts the minimum number of significant digits needed to preserve precision 100% of the time. Because the standard rounding rule for these two fundamental operations is accurate and completely safe for data, there is no need to extend this rule to keeping an additional significant figure as has suggested for multiplication and division.

PACS. 01.30.Pp - Textbooks for undergraduates.
PACS. 01.55.+b - Genreal physics.

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