Hi Guys, I'm not sure what the following question means. If you could help me out here it'd be really appreciated because my test for this subject is tomorrow! Please click on the attached thumbnail for the question. Many thanks in advance.
First check your knowledge of significant figures http://level1.physics.dur.ac.uk/skills/sigfigstest.php If you have difficulty watch this video http://video.google.com/videoplay?docid=-8711497301438248744 Since these are measurements, I presume that MPE = mean percentage error. Since you haven't stated any further information about the measurements (was there any?) I further presume that all the information is contained withing the listing and we must look at the number of significant figures stated. So the first one is stated to be 0.080. This means that the reading was between 0.079 and 0.081 (how many sig fig has this? ) This has four sig fig as both the leading zeros are needed So your measurement is really .080 +/- .001 So your max error is .001 So your MPE = 0.001/0.080 and MPE as a percentage is 0.001/0.080 times 100% Does this help?
Ok, let me try the next one. 4mV has 1 sig fig. So the reading is between 3 and 5. So the measurement is really 4mV +/- 1mV So the max error is 1mV The MP%E is (1/4)*100 = 25% And 3.0mA has 2 sig fig. So the reading is between 2.9 and 3.1 So the limits of accuracy is +/- 0.1mA The max error is 0.1 The MP%E is (0.1/3.0)*100 = 3.33% Is this correct?
I beg to differ. 0.079 and 0.081 each have only two significant figures. In decimal fractions, zero digits to the left of a nonzero digit aren't significant, although zero digits between nonzero digits are significant, as are zero digits to the right of nonzero digits. Mark
Mark. If this were a calculation and we were considering rounding errors I would agree with you. However this is a measurement in a practical subject, so I will quote directly from the Collins Reference Dictionary of Mathematics. (This also provides the alternative definition for rounding errors in calculation as one definition) "The digits of a number from the leftmost non zero digit to the righmost non zero digit. That is the largest to the smallest place value for which the coefficient is non zero. In some usages zeros with high place values are regarded as significant." I have emboldened the relevent passage. Let us say that the measurement was taken on a 0 - 10 amp meter. Then the first digit could have been 0,1,2,3...,9. Certainly the difference between 0.080 amps and 3.080 amps is very significant, as expoused in the dictionary. Only G W Bush would say that the leading zero is not significant if he gives you $0.08 change rather than $1.08.