A student asserts that rounding a result to the required significant figures after…
PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors
Problem
A student asserts that rounding a result to the required significant figures after every intermediate step gives the same final answer as rounding only once at the end. The following data are available to test the claim:
p=5.46,
q=2.3,
r=1.234.
The required computation is
y=pq+r.
(i) Calculate y by carrying all digits through the multiplication and addition, rounding only the final answer to its proper significant figures.
(ii) Repeat the calculation by first rounding the product pq to the appropriate significant figures before performing the addition. Then round the final result again to its proper significant figures.
(iii) Compare the two values obtained and explain, with reference to significant-figure rules, why any difference arises. State whether the student’s assertion is valid.