Significant Digits for the Sum of Three or More Numbers

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.

• Round as late as it is practical to do so. Sep 5 '13 at 15:31

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

• That's what I've done for a few years, however I recently had my attention brought to sigfigscalculator.appspot.com, which explicitly explains its answers, and sums the first two numbers , rounds, then repeats. Sep 5 '13 at 16:02
• 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 $5.56+5.56+2.5+2.5 = 16.1$ Sep 5 '13 at 17:09