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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.

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Rule 1: Addition and subtraction would always be to the lowest decimal points of the 2 variables. In your example, 2.354 + 0.002 = 2.356 would be 3 decimal points. You mentioned 3dp or 3sf. I think you meant 3dp or 4sf. Anyways, addition and subtraction should always be rounded to the variable with the lowest dp(in science). Another example to further illustrate this rule is, as you mentioned, 2.354 + 0.0002. We see 2.354 is the variable with the least accuracy(least decimal points of 3), so our answer would be 2.354(3dp).

Rule 2: While you did not ask this, it might help. Multiplication and division should be rounded to the variable with the least number of significant figures. For instance, 1.3 x 1.5 = 2.0(2sf) Why? Well, 1.3 x 1.5 = 1.95, which is 3sf. However, both 1.3 and 1.5 are 2sf. Hence, 1.95 has to be rounded to 2sf, which is 2.0. Let's say we have 2.354 x 0.0002. We get 0.0004708(4sf). Among 2.354 and 0.0002, the number with the least number of significant figures is 0.0002, with 1sf. Hence, we round 0.0004708 to 1sf, which is 0.0005.

Hope this helps.

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  • $\begingroup$ Thanks for your reply. I meant 4sf not 3sf, yes. However, regarding rule 2 the book says it should be the least number of sf not the highest. E.g. in 2.354*0.0002 according to the book the answer would be 0.0005 (1 sf). $\endgroup$ – Raghib Dec 29 '17 at 14:46
  • $\begingroup$ Oops sorry thanks for that, I will edit my post. Please check the tick if it helps. $\endgroup$ – QuIcKmAtHs Dec 29 '17 at 14:51

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