Significant figures: A classroom demonstration

Abstract

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 fig-& . ". ures recorded in the numerical measurement. students easilv com~rehend the significance of the first of these, o~e n o m i t or 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 NeededThe items needed to perform this demonstration are Two uncalibrated 1.000-m long sticks Two 1.000-m long decimeter sticks Two 1.000-m long centimeter sticks Two straight rods (wood or metal) that differ in 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~e of a different color, they are easily identifie'd'and do not'become a hazard if broken. The Classroom DemonstrationA 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 un--derstanding 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 ~roceed with 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-mar...

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