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5.D.2. Measurement ErrorsThere are two types of error that can occur whenmeasurements are taken: random and systematic.Random error results when an estimate is made toobtain the last significant digit for a measurement.The size of the random error is determined by theprecision of the measuring instrument. For example,when measuring length, it is necessary to estimatebetween the marks on the measuring tape. If thesemarks are 1 cm apart, the random error is greater andthe precision is less than if the marks were 1 mmapart. Systematic error is caused by a problem withthe measuring system itself, such as equipmentnot set up correctly. For example, if a balance isnot tared (re-set to zero) at the beginning, all themeasurements taken with the balance will have asystematic error.The precision of measurements depends on themarkings (gradations) of the measuring device.Precision is the place value of the last measurabledigit. For example, a measurement of 12.74 cmis more precise than a measurement of 127.4 cmbecause 12.74 was measured to hundredths of acentimetre, whereas 127.4 was measured to tenths ofa centimetre.When adding or subtracting measurements withdifferent precisions, round the answer to the sameprecision as the least precise measurement. Considerthe following:11.7 cm3.29 cm+ 0.542 cm15.532 cmThe first measurement, 11.7 cm, is measured toone decimal place and is the least precise. The answermust be rounded to one decimal place, or 15.5 cm.No matter how precise a measurement is, it stillmay not be accurate. Accuracy refers to how close avalue is to its accepted value. Figure 2 uses the resultsof a horseshoe game to explain precision and accuracy.(a) precise and accurate(c) accurate but not precise(b) precise but not accurate(d) neither accurate nor preciseFigure 2 The patterns of the horseshoes illustrate the comparisonbetween accuracy and precision.How certain you are about a measurement dependson two factors: the precision of the instrumentand the size of the measured quantity. Instrumentsthat are more precise give more certain values. Forexample, a measurement of 13 g is less precise thanone of 12.76 g because the second measurement hasmore decimal places than the first. Certainty alsodepends on the size of the measurement. For example,consider the measurements 0.4 cm and 15.9 cm.Both have the same precision (number of decimalplaces): both are measured to the nearest tenth of acentimetre. Imagine that the measuring instrumentis precise to ± 0.1 cm, however. An error of 0.1 cm ismuch more significant for the 0.4 cm measurementthan it is for the 15.9 cm measurement because thesecond measurement is much larger than the first. Forboth factors—the precision of the instrument usedand the value of the measured quantity—the moredigits there are in a measurement, the more certainyou are about the measurement.630 Skills Handbook NEL