I have a problem with significant figures. In an assignment, the paper gives us data to $3$ significant figures to calculate some values but afterwards requires us to calculate the percentage difference given an accepted value that is to $4$ significant figures. If we round the accepted value to $3$ significant figures as well, it yields $0 \%$ error. How should I deal with this?
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1$\begingroup$ More on significant figures. $\endgroup$– Qmechanic ♦Commented Aug 28, 2019 at 20:16
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That's the point, you weren't meant to round it up. Approximation of numbers comes with error because you are, for instance, adding .005 to 2.545 to approximate it to 2.55. The .005 has a value and adding it when it never existed generates error. Now the question is requesting you to calculate the percentage error (.005s) which I believe should be $$\frac {\sum errors}{\sum accurate} × 100$$
So approximation causes error.
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$\begingroup$ So do I use the calculated value to 4 s.f to compute the percentage error? $\endgroup$– aeol22Commented Apr 22, 2019 at 5:25
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$\begingroup$ Yes, it will then be the accurate value in the above formula. The sum of positive difference between the 3 s.f and 4 s.f will be the sum of error. $\endgroup$ Commented Apr 22, 2019 at 9:11