edited by GEORGE L. GILBERT Denison University Granville.OH 43023
tested demonstrcrtions Significant Figures: A Classroom Demonstration Submitted by: H. Graden Kirksey Memphis State University Memphis, TN 381 52 Checked by:
Paul Krause University of Central Arkansas Conway, AR 72032
Information about a measured property of matter is communicated by the magnitude of the numerical measurement, the unit for the physicalquantity employed to record the measured oro~ertv. . ". and the number of simificant figures recorded in the numerical measurement. students easilv com~rehendthe significance of the first of these, o ~ e n o m ior t neglect to record the second as a part of their measurement, and, along with some textbook authors, either carelessly regard or ignorantly disregard the third. The purpose of this classroom demonstration is to show students the function and importance of significant figures in a measurement. &
Materials Needed The items needed to perform this demonstration are Two uncalibrated 1.000-m long sticks Two 1.000-mlong decimeter sticks Two 1.000-m long centimeter sticks Two straight rods (wood or metal) that differin length by 1 em; e.g., 0.32 rn and 0.33 m.
Optional items are Two uncalibrated 1.000-yd long sticks Two 30-cm purchased rulers marked at each m m Two glass rods that differ in lengthby 0.5 mm; e.g., 27.23 cm and 27.28 m in length Two magnifying glasses
Six wooden sticks 1.000 m in length and two wooden sticks 1.000 yd in length must be prepared in-house. Calibration marks one decimeter apart on two of these meter sticks and one centimeter apart on two others can be drawn with a pencil. The two glass rods of near equal lengths are prepared by cutting two rods of equal length (about 27 cm) and fire polishing the ends. If one is not about 0.5 mm longer than the other. then shorten one rod bv heating - one end and gentlv . pressing it on a hard, flat surface. If each glass rod is wramed with t a ~ of e a different color, they are easily identifie'd'and do not'become a hazard if broken. The Classroom Demonstration A teacher, who is holding in each hand one metal or wooden rod, poses to the class, "Are the lengths of these rods identical?" Students accept the notion that no two rods are likely to have exactly the same length. The teacher then moves to the more important question, Wow many significant figures must he in the measurements of the lengths of these two rods in order to know that their lengens are different?"
Two students selected by the teacher are each given one of the two rods. Each student is to use an unmarked meter stick to measure the lenpth of his or her rod and record the result on the chalkboaid. The students can make their measurements onlv " bv " estimatine the rod's lendh - to the nearest tenth of a meter. This has been a learning experience for manv students in both estimating - lenbh - and understanding the uncertainty that exists as a part of every measurement. The lengths of these two rods cannot be distinguished by measurements having only one significant figure. Another measuring instrument must be employed to distinguish between them. The teacher can then ~roceedwith the demonstration by first selecting students to measure the rods' leueths bv use of a decimeter-marked meter stick (two sicnifiiant ffgures) and finally by using a centimeter-marke-d meter stick (three significant figures). Only when the lengths are measured to three significant figures can the two rods be distinguished. Some students usually suggest that it would be easier to determine if the lengths of the rods differ by avoiding measurement altogether. By standing the two rods on a table top, a person could easily identify the taller rod. Sure, but this is a measurement. It is the comparison of the length of one rod with the leneth of the other rod rather than with the length of another arbitrary standard. All measurements are a comoarison of a Dhvsicd ~ r o ~ e roft vone obiect with that of a s&dard, whilh &ll always yieid a measurement havine a n uncertaintv and a unit. Onlv counting. -. a one-to-one correspondence between items and integers, could vield a numerical result without an uncertainty and a unit of a physical quantity. Upon standing the rods side-by-side on a tabletop, one of the rods is perceptibly longer than the other. This demonstration shows the students how much the lengths of two rods may differ and yet require a measurement of three simificant fieures in order to distineuish between them. ~ i u l standiLg d the rods side-by-sidelbean acceptable way to determine the loneer if one rod were in MemDhis and the other in New ~ r l e a n s ?
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Options To Consider The teacher may alter or extend this demonstration. First, after the students have measured the lengths of the wooden or metal rods to one significant figure, ask them to repeat their measurement by use of an unmarked yardstick. The class should observe that a measurement of onlv one significant figure is all that can be obtained by use i f either of these instruments. but the unit em~lovedto record the measurements will certainly be diffe;ent. The demonstration may be stopped at this point if the single purpose is to show that the system of units employed to describe a measurement does not improve the accuracy of a measurement. A second option is open to teachers who feel that their students need a bigger challenge. The teacher can show the class two new rods side-by-side that have lengths so close that the class cannot distinguish the longer. The teacher can ask the class, "Could a measurement having four significant figures distinguish between the lengths of these two rods?" Volume 69 Number 6 June 1992
497
Select two students to measure the lengths of the glass rods by use of purchased meter sticks with calibration marks at each millimeter of length. The students can swap meter sticks andlor rods and measure the lengths again. Almost all students need to be instructed about parallax errors during this demonstration. If the zero point of the metric rule is not at the ruler's end, or if the end is worn, shouldbe reminded that they shouldnot meathe sure a length beginning at the extreme end of the ruler. students able to measure lengths to four significant figures can show that the two rods do have different lengths.
498
Journal of Chemical Education
During these demonstrations students observe that two rods that are obviously different in length are the same length to one and even two significant figures, but two rods that appear side-by-side to be the same length can be to have lengths if measurements of their lengths are made correctly to four significant figures, The teacher has several opportunities to teach important howledge about significant figures, units, measurements, and the uncertainty of measurements during this series of demonstrations.
