ErrorAnalysis

ErrorAnalysis - Error Analysis and Significant Figures (from

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Error Analysis and Significant Figures (from http://www.owlnet.rice.edu/%7Elabgroup/pdf/Error_analysis.pdf) No measurement of a physical quantity can be entirely accurate. It is important to know, therefore, just how much the measured value is likely to deviate from the unknown, true, value of the quantity. The art of estimating these deviations should probably be called uncertainty analysis, but for historical reasons is referred to as error analysis. This document contains brief discussions about how errors are reported, the kinds of errors that can occur, how to estimate random errors, and how to carry error estimates into calculated results. SIGNIFICANT FIGURES Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m. ABSOLUTE AND RELATIVE ERRORS The absolute error in a measured quantity is the uncertainty in the quantity and has the same units as the quantity itself. For example if you know a length is 0.428 m ± 0.002 m, the 0.002 m is an absolute error. The relative error (also called the fractional error) is obtained by dividing the absolute error in the quantity by the quantity itself. The relative error is usually more significant than the absolute error. For example a 1 mm error in the diameter of a skate wheel is probably more serious than a 1 mm error in a truck tire. Note that relative errors are dimensionless. When reporting relative errors it is usual to multiply the fractional error by 100 and report it as a percentage. SYSTEMATIC ERRORS Systematic errors arise from a flaw in the measurement scheme which is repeated each time a measurement is made. If you do the same thing wrong each time you make the measurement, your measurement will differ systematically (that is, in the same direction each time) from the correct result. Some sources of systematic error are: • Errors in the calibration of the measuring instruments. • Incorrect measuring technique: For example, one might make an incorrect scale
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This note was uploaded on 10/19/2011 for the course CHEM 197 taught by Professor Bonk during the Summer '11 term at Duke.

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ErrorAnalysis - Error Analysis and Significant Figures (from

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