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The question says to give your answer to the following calculation in scientific notation with the correct number of significant figures:

$(1.285 \times 10^{-2}) + (1.24 \times 10^{-3})$. The answer is $1.409 \times 10^{-2}$. Wouldn't it be $1.41 \times 10^{-2}$, because the minimum sig. figs. is $3$ [in the $1.24$] instead of the answer, which is $4$ sig. figs.?

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    There are some rules in this regard, but few people take them seriously. And it's not a big deal2017-01-31

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No, when you add you stop at the first column that doesn't have an entry from some number. Here we have $$\begin {align}0.01285\\ \underline{+0.00124}\\ 0.01409 \end {align}$$ The rule about counting significant figures is for multiplication, where you want to consider fractional accuracy. For addition you want to consider absolute accuracy. In this case each number is assumed to have a potential absolute error of $\pm 0.000005$