On Significant Figures The proper use of significant figures is freNumber Number quently a source of confusion to both the undergraduate and graduate student. In particular, the of Signi- Relative o f signi~elative ficanf Uncerficanf Uncerrules governing the significance, or lack thereof, of Number Figurer tainty zero digits, sometimes appear arbitrary and a matter Number Figurer tainty of sheer memorization. These rulesean be summa- 0.006og 3 11609 609 3 1,609 rized in asinglestatement which is hothoperation- 0.0609 3 1/609 0.6090 4 116090 3 11609 609.0 4 116090 ally simple to apply and educationally instructive 3 1/609 4 116090 6090 to the user. I personally find thedefinition presented 60.9 3 1/609 6090.0 5 1/60900 below ta be unamhiguous and more lucid than those presented in most analytical chemistry textbooks. Realizing that the essential feature of significance relates to relative uncertainty,' the statement is: "Zeros (like other digits) are significant, if and only if, their removal changes the relative uncertainty of the number." Using this definition one can immediately rationalize the data in the following table. This statement is pedagogicallyhelpful in that it teaches the essential criterion of significance, namely, relative uncertainty.' For an ambiguously stated number such as 6090, which ends in a zero digit but contains no decimal paint, no rule can specify the number of significant figures without one having prior knowledge of the intended meaning of that number. Such amhiguity can, of course,_beavoided hy expressing the number in scientific notation, e.g. as 6.090 X lo3 or 6.09 x 103 or by writing it as 6090. or 6090 etc.
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'Pinkerton, R. C., and Gleit, C. E., J. CHEM. EDUC., 44,232 (1967). Flaschka, H. A,, Barnard, Jr., A. J., and Sturrock, P. E., "Quantitative Analytical Chemistry," Barnes and Noble, Inc., 1969, vol. 1, p 4. Colorado School of Mines Golden, Colorado 8Ullll
578 I Journal of Chemical Education
Patrick MacCarthy
