Five independent length measurements are to be combined according to the expression x…

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

Five independent length measurements are to be combined according to the expression x=(a+b) cd−e.x = \frac{(a + b)\,c}{d - e}. The recorded values are: a=12.158 ma = 12.158\,\text{m}, b=0.37 mb = 0.37\,\text{m}, c=3.6 mc = 3.6\,\text{m}, d=4.521 md = 4.521\,\text{m}, e=1.02 me = 1.02\,\text{m}. (i) Evaluate the numerator (a+b) c(a + b)\,c and quote it with the correct number of significant figures. (ii) Evaluate the denominator (d−e)(d - e) and state it with the proper significant figures. (iii) Using the values obtained in (i) and (ii), compute xx and write the final answer in scientific notation with the correct significant figures. Show clearly how you decide the number of significant figures at each stage of the calculation.

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