When adding with differences in significant figures, should you round first?

Question

For example, $3.4698 + 2.11 = 5.57$ according to the rules shown in Wikipedia. But in reality, it is closer to $5.58$, as $3.4698$ can be rounded to $3.47$. So which is the correct method?

I would say 5.58. I tend to carry one extra digit through all of my preliminary calculations to avoid the errors introduced by repeated rounding. But rounding is an estimate and estimates have errors. If the last place is off by 1, should you really care. If it is off by several the you have a problem. — Doug M, Apr 06 '18 at 03:51
So, if you're rounding to the nearest whole number 3.4+.3.4=6? Round at the end. — saulspatz, Apr 06 '18 at 03:59
If you are going to reference Wikipedia, you should quote it or at least provide a link. — Ross Millikan, Apr 06 '18 at 04:02
This question is well answered in Physics Stack Exchange. See this question - Do you round off insignificant digits in the middle of a calculation?. Even though it explains for multiplication, the same applies for addition or subtraction. — Vishnu, Nov 11 '19 at 15:51

score 0 · Answer 1 · answered Apr 06 '18 at 04:01

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The rule from Wikipedia is " the result is rounded to the last digit that is significant in each of the numbers being summed.". You perform the calculation with all the numbers you have and round the result. This would give $5.58$ in your example.

answered Apr 06 '18 at 04:01

Ross Millikan

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When adding with differences in significant figures, should you round first?

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