Calculators and Significant Figures The advent of inexpensive calculators has had a major impact on college chemistry courses, especially a t the first year level. While debate continues as to the use of calculators in exams, a far more serious problem (to my mind) has arisen in the computation of laboratory and homework exercises-that of significant figures. The complete lack of respect for the limitations of experimental measurements on computed results i s directly attributable, I feel, to the calculator screen displaying eight or ten digits. To combat this problem, I have devised the fallowing demonstration. The only materials required are a mm ruler. a iournal sooroximatelv ,the size of the Journal of Chemieol Edueotion. and a calculator. Five sludenlu are tailed to the front of the elnss. Aftpr receiving detnlled instructims i m ertimatint: meaiurements 10 the001 cm, each student ia askrd lo measure the length. width, and thickness d t h e jt,urnal. K a ~ hmeaiuremcnt ir tabulated as rhuun in the tahlt.. CGna avalculatur. the front coversurfaceareaand thevolwneotrhe jaurnalareralr~tlnted.Typ~rnl ~
~~
~
Length Icm)
~
~ ~~ .. .
Width (cml
~
,
Area lcrn*)
Thickness (cm)
v o l u m e (crn')
These calculations graphically illustrate the necessity of limiting the numbers of digits reported in a computed result and lead into further discussion of'significant figures, random errors, etc. The demonstration has been used in several freshmen classes near the start of the course. and once in a ohwical chemistrv course near the middle of a semester. The . freshmen classes were then given general instructims on estimating the appropriate numhtr uf s~gnif~rant figurea on o empured answer hy cxaminatiun of the factors "red in the ralculatrm The physical chernirtry rhss applied a prupngntwn of errors analysis (which works extremely well for this exercise). In each ease the results were very gratifying asmarked improvement in the use of significant figures was observed. Two other points should he noted. First, use only one ruler. The inexpensive rulers can vary by as much as 2 mm over a 20 cm range. Second, use the bound edge of the Journal to measure the thickness. The measurements have better reproducibility.
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Washington College Chestertown, Maryland 21620
L a r r y C. Satek
Volume 54, Number 3, March 1977 / 177
