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How Many Digits Should We Use in Formula or Molar Mass Calculations?

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Christer Svensson

Department of Chemistry and Biomedical Science, University of Kalmar, 391 82 Kalmar, Sweden

J. Chem. Educ., 2004, 81 (6), p 827

DOI: 10.1021/ed081p827

Publication Date (Web): June 1, 2004

Section:

History, Education, and Documentation

Abstract

This article addresses the question often asked by students, â€œHow many digits should I use when calculating the formula or molar mass of a substance?â€ Three rules of increasing complexity are proposed and discussed. Elementary propagation of error theory is applied and the accuracy of recommended atomic weights as well as the accuracy of elementary laboratory work is considered. The first rule is to use four digits in atomic weights and consider the calculated formula or molar mass as given with four significant digits. This rule is appropriate for beginners but has some disadvantages. The second rule is to use all digits in the recommended atomic weights and to estimate the accuracy of the result from the number of decimal places or significant digits in these. The third rule is to use all digits in the recommended atomic weights and to calculate the absolute maximum uncertainty of the result from the recommended uncertainties of the atomic weights. The uncertainty is rounded up to one (two) significant digit(s), and the formula or molar mass is rounded to the same absolute accuracy as the rounded uncertainty.