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When adding three or more numbers together do you add two at a time, while applying significant digits to each sum of two, or do you sum the whole thing, then modify it to express the significant digits.

For example, which of the following is correct:

$2.5 + 2.5 + 5.56 + 5.56 = 5.0 + 5.56 + 5.56 = 10.56 + 5.56 = 16.12 = 16.1$

$2.5 + 2.5 + 5.56 + 5.56 = 5.0 + 5.56 + 5.56 = 10.6 + 5.56 = 16.16 = 16.2$

Note that to $10.56$ is $10.6$ in the second equation, since $5.0 + 5.56 = 10.12$, rounded to $10.1$, since $5.0$'s least significant is a tenth.

Nathan
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1 Answers1

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Add all the numbers together at the full precision then round to the required number of digits

$2.5+2.5+5.56+5.56 = 16.12$ which is $16.1$ to 3 significant figures

Warren Hill
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  • That's what I've done for a few years, however I recently had my attention brought to http://sigfigscalculator.appspot.com, which explicitly explains its answers, and sums the first two numbers , rounds, then repeats. – Nathan Sep 05 '13 at 16:02
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    That makes the order important $2.5+2.5+5.56+5.56 = (2.5 +2.5) + (5.56+5.56) = 5.0 + 11.12 = 16.1$. Just tried that site $2.5+2.5+5.56+5.56 = 16.2$ while $5.56+5.56+2.5+2.5 = 16.1$ – Warren Hill Sep 05 '13 at 17:09