Question

The "best" result is always associated with the measurement with the smallest uncertainty. Measurement B has half the standard uncertainty of measurement A. Therefor e our 68 % coverage probability is associated with a smaller interval (83.44 g o 83.56 g) for measurement B than measurement A (83.38 g to 83.62 g). In other words we have better knowledge about the value of the measurand from measurement B, since we have the same coveroge probability associated with a norrower interval. 4.3 Reporting the result of your measurement When reporting the result of a measurement, it is better to provide too much information rather than too little. For example, you should describe clearly the methods used to calculate your uncertainties, and present the data analysis in such a way that each of the important steps can be easily followed by the reader of your report. When reporting the result of a measurement, you should therefore give: (i) a clear statement of the measurand: and (i) the best approximation of the measurand and its standard uncertainty (remember to give the units). Sometimes it is also necessary to state the coverage probability (see Appendix H) For example, the result of the measurement may be reported as: ..the best approximation of the mass was determined to be 83.45 g with a standard uncertainty of 0.34 g (with a 68% coverage probability, using a Gaussian pdf)." You can now report your final results for the four examples given on the previous pages. Complete the information below. This is how you should always the result of a measurement. (a) t ( 68 % coverage probability) ( 68 % coverage probability) ( 68 % coverage probability) _ mA ( 68 % coverage probability) cm (b) f (c) V: Hz t _ V _ (d) I-_ - _ 4.4 Significant digits If we determine a particular measurement result (after a series of calculations) to be m 35.82134t 0.061352 kg, how many digits should we quote in our result ? The uncertainty of 0.061352 kg tells us that we are uncertain about the second decimal place in 35.82134 kg Our final result is then written as m 35821 : 0.061 kg

Answer 1

4.4:

l -> 34.47 $\pm$ 0.4572 becomes 34.47 $\pm$ 0.46

the uncertainty shows we are not sure about the 1st decimal rounding the uncertainty to two significant figure becomes 0.46

f-> 41074 $\pm$ 25.9 -> 41074 $\pm$ 26 ; we are not sure about the 10th place

k-> 1.3743 x10⁵$\pm$ 216 we are uncertain about the hundredth place

it becomes 137430 $\pm$ 220 or (1.3743 $\pm$ 0.0022) x10⁵  

I -> 23274.64746 $\pm$ 5.566 becomes 232747.6 $\pm$ 5.6

we are uncertain about the 1s place , rounding the uncertainty to 2 digits it becomes 5.6

4.5

0s to the right of the decimal have no value, the least quantity we could measure is 1/10 mm , this values is significant to the first decimal place. reporting a result to 2nd decimal place does not make any sense as we did not measure anything to the 2nd decimal place.

writing extra digits which are insignificant makes no sense.