Test Bank for Financial Statement Analysis and Security Valuation, 5th Edition

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1REVIEWMEASUREMENT AND CALCULATIONS IN CHEMISTRYQuestions1.A random error has equal probability of being too high or too low. This type of error occurswhen estimating the value of the last digit of a measurement.A systematic error is one thatalways occurs in the same direction, either too high or too low.For example, this type oferror would occur if the balance you were using weighed all objects 0.20 g too high, that is, ifthe balance wasn’t calibrated correctly.A random error is an indeterminate error, whereas asystematic error is a determinate error.2.Precision: reproducibility; accuracy: the agreement of a measurement with the true value.a.Imprecise and inaccurate data: 12.32 cm, 9.63 cm, 11.98 cm, 13.34 cmb.Precise but inaccurate data: 8.76 cm, 8.79 cm, 8.72 cm, 8.75 cmc.Precise and accurate data: 10.60 cm, 10.65 cm, 10.63 cm, 10.64 cmData can be imprecise if the measuring device is imprecise as well as if the user of themeasuring device has poor skills. Data can be inaccurate due to a systematic error in themeasuring device or with the user. For example, a balance may read all masses as weighing0.2500 g too high or the user of a graduated cylinder may read all measurements 0.05 mL toolow.A set of measurements that are imprecise implies that all the numbers are not close to eachother. If the numbers aren’t reproducible, then all the numbers can’t be very close to the truevalue. Some say that if the average of imprecise data gives the true value, then the data areaccurate; a better description is that the data takers are extremely lucky.3.Accuracy refers to how close a measurement or series of measurements are to an accepted ortrue value.Precision refers to how close a series of measurements of the same item are toeach other (reproducible). The results, average = 14.91 ±0.03%, are precise (are close to eachother) but are not accurate (are not close to the true value).4.Volume readings are estimated to one place past the markings on the glassware.Theassumed uncertainty is ±1 in the estimated digit.For glassware a, the volume would beestimated to the tenths place since the markings are to the ones place.A sample readingwould be 4.2 with an uncertainty of ±0.1.This reading has two significant figures.Forglassware b, 10.52 ±0.01 would be a sample reading and the uncertainty; this reading has foursignificant figures.For glassware c, 18 ±1 would be a sample reading and the uncertainty,with the reading having two significant figures.5.Significant figures are the digits we associate with a number. They contain all of the certaindigits and the first uncertain digit (the first estimated digit). What follows is one thousand

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