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It is a simple one but different teachers answer this question differently. $$34+1.4+0.2$$ what would be its answer with due regards to significant figures?

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The answer is 36. You do the addition to get 35.6, but then you realize that you have an uncertianty of about .5 on this answer because the 34 had an uncertianty of about .5, so it doesn't make sense to give the first decimal place because you aren't sure about it, so you round 35.6 to 36.

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  • $\begingroup$ your answer makes sense but can u please explain the uncertainty of 34. $\endgroup$
    – elle
    Commented May 2, 2014 at 18:20
  • $\begingroup$ The reason that it is written as 34 and not 34.0 is because you are not sure that the digit after the decimal point is really supposed to be zero. the number might really be 34.3, or it might be 33.8 or anything around there. Thus the sum might not really be 35.6, it might actually be 35.9 or 35.4. So you are not sure about the decimal in the sum either. Therefore you don't write the decimal. Instead, you round the number. $\endgroup$ Commented May 2, 2014 at 18:27
  • $\begingroup$ but if we write the decimal our error% will be less as compared to 36. $\endgroup$
    – elle
    Commented May 2, 2014 at 18:32
  • $\begingroup$ I don't understand what you are saying. Are you saying it looks like we know more if we write the decimal? I agree with that. But we don't know enough to write the decimal. $\endgroup$ Commented May 2, 2014 at 18:35

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