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5.D. Uncertainty inMeasurementThere are two types of quantities used in science: exactvalues and measurements. Exact values include definedquantities: those obtained from SI prefix definitions(such as 1 km = 1000 m) and those obtained fromother definitions (such as 1 h = 60 min).Exact values also include counted values, such as5 beakers or 10 cells. All exact values are consideredcompletely certain. In other words, 1 km is exactly1000 m, not 999.9 m or 1000.2 m. Similarly, 5 beakerscould not be 4.9 or 5.1 beakers; 5 beakers are exactly5 beakers.Measurements, however, have some uncertainty.The uncertainty depends on the limitations of theparticular measuring instrument used and the skillof the measurer.5.D.1. Significant DigitsThe certainty of any measurement is communicated bythe number of significant digits in the measurement.In a measured or calculated value, significant digitsare the digits that are certain, plus one estimated(uncertain) digit. Significant digits include all thedigits that are correctly reported from a measurement.For example, 10 different people independentlyreading the water volume in the graduated cylinder inFigure 1 would all agree that the volume is atleast 50 mL. In other words, the “5” is certain.However, there is some uncertainty in the nextdigit. The observers might report the volume asbeing 56 mL, 57 mL, or 58 mL. The only way to knowfor sure is to measure with a more precise measuringdevice. Therefore, we say that a measurement such as57 mL has two significant digits: one that is certain(5) and the other that is uncertain (7). The last digitin a measurement is always the uncertain digit. Forexample, 115.6 g contains three certain digits (115)and one uncertain digit (6).100 mL908070605040302010volume of waterand solidvolume of water100 mLvolumeof solidFigure 1 This figure shows the difficulty of making observationsusing an imprecise measuring device.Table 6 provides the guidelines for determining thenumber of significant digits, along with examples toillustrate each guideline.908070605040302010Table 6 Guidelines for Determining Significant DigitsGuidelineCount from left to right, beginning with the first non-zero digit.Zeros at the beginning of a number are never significant.All non-zero digits in a number are significant.Zeros between digits are significant.Zeros at the end of a number with a decimal point are significant.Zeros at the end of a number without a decimal point are ambiguous.All digits in the coefficient of a number written in scientific notation are significant.ExampleNumber Number of significant digits345 3457.35 50.235 30.003 11.1223 476.2 2107.05 50.02094 410.0 3303.0 45400 at least 2200 000 at least 15.4 × 1​0​ 3 ​ 25.40 × 1​0​ 3 ​ 35.400 × ​10​ 3 ​ 4628 Skills Handbook NEL