In The Last Right-Hand Digit

So you've covered the rightmost digit greater and less than 5. What if it is 5?

Answer, round to the even next digit. .375 (to 2 places)=.38. .625 (to 2 places)=.62

If 5 or more, round up.

I've never heard before of rounding to the even digit; what would the rationale be? (I can think of one, but want to see what others there might be.)

One reason for rounding 5 up is the closer ratio of rounded to real value; e.g. if you round 25 down to 20, ratio is 4:5; if you round 25 up to 30; ratio is 5:6, which is closer to 1.

I had quite a discussion about this with a co-worker several years ago. I contacted ASTM to see if they had a standard, and they referred me to IEEE. IEEE does, in fact, say to round to the even number if the rightmost digit is 5. I'm afraid I don't recall the standard.

The best explanation I can give is that many dimensions are diameters or features arranged symmetrically about a centerline, and this allows the dimension to be divided by 2 without adding a decimal place. It also allows, if you're using inches in the screwed up manner we do in the US, fractions to be converted to decimals and, usually, add up the same way as the fractional equivalent. For example, 3/8 + 5/8 = 1 and .38 + .62 =1.00

Actually, there are several ways to round in this situation. Go to the Wikipedia link on this thread for a fuller explanation and the IEEE standard number.

I left this out. Some CAD programs (SolidEdge, for example), round this way. Others (AutoCAD follow the "greater than or equal to 5" rule.

Read it carefully

I think you have already asked this question? (similar)

if you have something say 20.0 ≠ 0.2

and you get a value 20.243 then this value will be rounded to the right most digit of the specification (ie .X)

and the rounded value 20.2 will be checked against specification (in this case it will meet the spec)

whereas 20.253 will be rounded to 20.3 and will fail.

This is just explaining T (as we learnt some 30 years back in fact I remember the cut off was not always 0.5 there was another system where the square root was the cut off value ie around 0.316, I am not sure where that is used since in practice we always see the 0.5.

You are referring to ASTM E29. You should purchase a copy.

Thanks for the help. I am doing a favor to my friend who is capable (or really?)but not willing to spend time and efforts to do some research into this. Actually, rounding off method is a deceptively simple topic. One can easily be cheated into believing that it is not worthy of doing much reserach into it. But "disaster" can happen and here it is what wiki says:

http://en.wikipedia.org/wiki/Rounding

Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in 1982. It was initially set at 1000.000, and after 22 months had fallen to about 520 — whereas stock prices had generally increased in the period. The problem was caused by the index being recalculated thousands of times daily, and always being rounded down to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating with better rounding gave an index value of 1098.892 at the end of the same period.^[1]