On rounding off numbers?

Question

About 21 hours ago, 'beautiful1213' posed a question in CHEMISTRY, "Can someone help me with chemistry?" having to do with rounding off _.5 numbers...up, down (or sideways? lol).

This has led to a small debate, which is really the province of this section. Can I get one of you experts to review this question and comment thereupon?

Preferably, post your answer both here (10 points for best answer) and there (to resolve this matter and not lead chemists astray.)

Answer 1

Back many years ago, the rule was to round the .5s to the EVEN number.  That way half the time you would be going down, and half going up.

Answer 2

A link to the question would sure be helpful.

Answer 3

Rounding to even is as good a rule as any.  You wouldn't be rounding if there had been anything to choose between rounding up and rounding down in one particular case, and an impartial rule like this makes the accumulation of rounding errors unlikely.

As I am sure the questioner knows, in serious measurement one quotes size of probable error, rather than relying on just counting significant figures.  There are then things called "Rules for the propagation of errors" (I am not making this up) to combine the uncertainties of different measurements.

I suspect the questioner would agree with me in sympathising with the chemistry teachers who get to teach the "significant figures" version of this when they would rather be teaching chemistry.