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I thought you round to the same place as the number with the addend with the least precision. For example, if you had $25.63+ 42.3$ the answer would be rounded to the tens place ($67.9$).

However, my chemistry teacher just said that it would be rounded to the same place as the number with the least places after the decimal point. Is this true?

For example, if I added 100+32, would it be rounded to the ones place (because there are no digits after the decimal point) or would it be rounded to the hundreds place (because 100 has the lowest precision, with its only sigfig in the hundreds place)?

Thanks.

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2 Answers 2

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Rounding rules are pretty arbitrary, with their goal being to lose as little information as possible.

The results also depend on how accurate the inputs are. For example, for "100+32", if nothing is stated about the inputs, I would assume that the answer is 132, since I would assume that the 100 is exact.

If the inputs are not exact, there are either implicit or explicit error bounds. For example, if that 100 were known to two figures, the units digit would be in doubt, and you could write it as "$100\pm 5$" (or "105$\pm$5").

With regards to what your instructor said, they said "after the decimal point." This assumes that all the figures to the left of the decimal point are correct.

There is a lot more that I could say, but that's enough for now.

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If your example had been $$0.26 (2\text{ sig.fig. or }2 \text{ decimal places})+42.3 (3\text{ sig.fig. or }1 \text{ decimal place})$$ your chemistry teacher would have advised an answer of $42.6 (1 \text{ decimal place})$.

As for adding $100$, it depends on how accurately this was measured. Was it rounded to the nearest $100$, nearest $10$, nearest $1$ or nearest $0.1$?

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  • $\begingroup$ It was given as 100g, so I can only assume 1 sigfig. $\endgroup$ Oct 7, 2015 at 23:48
  • $\begingroup$ If you assume that then adding or subtracting less than $50g$ will not change the rounded result. But it is a strong assumption $\endgroup$
    – Henry
    Oct 7, 2015 at 23:49

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