# Significant figures when adding and subtracting

In my book (Tipler and Mosca) it says that the number of significant figures when adding or subtracting is the same as the position of the last decimal place where both numbers have significant figures.

For example, 2.354+0.002. Here, the last decimal place for which both have a significant figure is the third, so the answer would be 2.356.

Another example: 2.354+0.02. Here, the last decimal place for which both numbers have a significant figure is the second, since 0.02 doesn't have a significant figure beyond the second decimal place even if 2.354 does. Therefore, the answer is 2.37.

However, I thought of a sum where this doesn't work: 2.354+0.0002. Here, "the last decimal place for which both numbers have a significant figure" doesn't exist, since the first significant figure of 0.0002 is in the fourth decimal place, but 2.354 doesn't have any decimal places beyond the third decimal place. How would we deal with this situation?

Another question I had is how do we write the result? For example, for 2.354+0.002=2.356 would I put (3 sf) after it, or would it be (3 dp) instead? The rule doesn't seem to explicitly state what the significant figures of the result would be, it simply tells us how to numerically work out the result to get 2.356.

Edit: This is about the comment I made on this post using a guest account. I am able to post again on my normal account. Not sure what happened.