How Many Significant Digits in 0.05'C? J a m e s D. Power Unioer.sity of Petroleum & Minerals Dhahran, Saudi Arabia We often express results in the form x f Ax, where Ax is the uncertainty. The relative uncertainty is A d x . Generalizing the aonroach of Pinkerton & Gleit. (J. CHEM. EDUC., 44.232 (196:i) we can define the numher of significant digits (S.D.) in x as B - logt,(Ax/x), where B is an arhitrary constant. For example, if we choose B = 1, then 10.0 f 0.1 has exactly 3 S.D., and 9.9 f 0.1 has 2.996 S.D. The way iudge the precision . we . of x partly depends upon how x is used in subsequent calculations. If it is just subtracted from another value, then only Ax is important, and the relative uncertainty and number of S.D. are irrelevant. Counting the numher of S.D. in a result is meaningful only if using absolute units, with zero as the smallest possible value. Chaneine the size of the hase unit. such as from cm to m. mult&li& both Ax and I by the same factor, and hence does not change the numher of S.D. We use many non-absolute linear scales, such as Celsius and Fahrenheit temperatures, standard electrode potentials, relative potential energy, standard free energies and enthalpies of formation, etc. The choice of zero on such scales is an arbitrary convention, with 1111 physical signitimnw:. A linear transiurmarion to u new scnle cannot nffect thv precisiun ofour results. Thus.0.05 0.0IoC = :32.09 f U . W " . and it is fallacious to aicritw 11 number of S.DT to either of these values. With anv scale. we can use the convention that the final digit recorded is uncertain and preceding digits certain. The numher of decimal places recorded implies the approximate magnitude of Ax. Since an uncertainty o f f O.l°C corresponds to f0.18OF ..: f0.2'F, the results in "C to OF conversions should be rounded to the same numher of decimal places as were given in the initial temperature. This seems simple and obvio&, but our textbooks abound with erroneous examples, such as 33°F = 0.56"C. In all theoretical equations, any quantities measured on a non-absolute linear scale will appear as differences. The arbitrary zero of the scale cancels in the subtraction, and the
result is the same as if we had used an absolute scale with the same size of unit. For example, our choice of the standard hydrogen electrode cancels when we calculate the emf of a cell, and we can use relative uncertainty and numher of S.D. to describe the precision of this emf.
Acne Lotion-Great for Pimples and Making Polymers! J e f f r e y May Wayland High School Wayland, Massachusetts from Schools have been advised to remove benzovl . ~eroxide . their stockrooms, useful though it is for initiating the polymerization of methymetharrylate. The preparation of acrylic plastic trom this monomer isa nice lah, t ~ uitt is not worth the t r o ~ ~ bof l e keeping the potentially explmive initiator around. Yet this substance has found its place on a new shelf-in the teenage consumer's medicine cabinet. ~ e n z operoxide ~l is being used increasingly in acne creams and lotions. For years, i t was used in certain lotions a t concentrations of 5% or less. These lotions have become more popular, and perhaps due to competition, the percentage of benzovl oeroxide in them is soiraline UD. Benoxvl," a lotion made"b;~tiefel Labs, contains lo%iu;pended &id peroxide. Teachers can take advantage of this boom. The corner drug store is now a ready supplier of small amounts of henzoyl peroxide. It can he separated easily from the mixture it is in as long as the lotion is the greaseless type. Just add about 15 volumes of water to one volume of the lotion in a test tube. Shake gently to disperse the suspension and wait for the white solid to settle. Decant the water awav. and add a small amount of alcohol to resuspend and transfeithe insoluble solid. Filter and allow the solid to dry (away from any source of heat or sparks). T h e powder should be handled with caution, and i n small amounts only. I t is highly inflammable and i n large amounts, under certain conditions, c a n detonate. (Note: To this author's knowledge, there have not been any reports of overzealous teenagers betonating pimples away after over-application of acne lotion).
Volume 56. Number 4, April 1979 / 239
