In my chem class the other day, we were working through a question about average atomic mass. We were given the following information about two isotopes of boron:
Boron-10: Atomic Mass = 10.013, % in nature: 19.8%
Boron-11: Atomic Mass = 11.009, % in nature: 80.2%
For the weighted average (before sig fig rounding), then, Boron 10 contributes 10.013*.198 = 1.982574 AMU, and Boron 11 contributes 11.009*.802 = 8.829218 AMU.
Now, if we were just finding one of these values, we would report 1.98 or 8.93 AMU (to 3 sig figs). Adding these together, we get 10.81 AMU. However, if we follow "convention" and do all rounding at the end, we get 10.8 AMU (3 sig figs).
My question is, which of these is correct? On the one hand, 10.8 is correct since it has the same number of sig figs as the least accurate given value (19.8% or 80.2%). On the other, why should we go from hundredths to tenths precision just because we got a new digit in the least precise position? One could argue that the "10" is essentially its own digit.
Personally, I agree with the response here (Significant Figures Interpretation) that says sig figs don't make a whole lot of sense. But for the purposes of this question, which is the proper way to express the answer?
Thanks in advance!