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There are actually two ways given to add or subtract significant figures in different books .In books like concepts of Physics by HC Verma it is written that round of the numbers given first and then add or subtract them but in others book it is written to add the numbers first and then round of the answer. Usually the answer is same but sometimes the answer is different for example while adding 24.36 + 0.0623 + 256.2 answer will come different both the times when we perform by both ways.

So what is the correct way to add or subtract significant figures?

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  • $\begingroup$ Related: physics.stackexchange.com/questions/162721/… $\endgroup$
    – Gabriel Ybarra Marcaida
    Commented May 1 at 8:54
  • $\begingroup$ What did H C Verma say is wrong with doing the rounding at the end? $\endgroup$
    – Farcher
    Commented May 1 at 11:36
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    $\begingroup$ There is no correct way since significant figures are entirely made up. They are just a simplifying approximation to the reality called error propagation, which involves multi variable calculus. $\endgroup$
    – Matt Hanson
    Commented May 1 at 11:58
  • $\begingroup$ Hc verma didn't say its wrong to do the rounding at the end , it's just that the answer is different when we do the round at the end and when we round off each number individually for example while adding 24.36 + 0.0623 + 256.2 answer will come different both the times when we perform by both ways. $\endgroup$
    – ARNAV CHADHA
    Commented May 2 at 21:15

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The correct way to add or subtract significant figures is the way that your instructor teaches. Significant figures are not used by professional scientists at all. They are only used in introductory classes for instructional purposes, so they should be used with the convention specified by your instructor.

Professional scientists explicitly state their errors and use the propagation of errors, as described in the BIPM's "Guide to the Expression of Uncertainty in Measurement". For your example, in a scientific publication you would write: "$24.360(5) + 0.06230(5) + 256.20(5) = 280.62(5)$ where the numbers in parentheses are the numerical values of the standard uncertainty referred to the corresponding last digits of the quoted results."

In other words, $24.360(5)$ means that if you measured this value repeatedly you would get a mean of $24.360$ and a standard deviation of $0.005$. (I am assuming that is what your significant figures mean, but it is ambiguous which is why they are not used professionally).

So the sum means that if you repeatedly measure the sum you would get a mean of $280.62$ with a standard deviation of $0.05$. This is how the uncertainty would be characterized in a scientific publication.

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