Good morning/afternoon,

I was uncertain as to whether a number such as 85.25 rounding to the nearest tenth would be 85.3 or 85.2. I thought I had heard somewhere that if 5 is the last number that you don't round up. But I have also heard that anything 5 and above you do round up. It's been awhile since I've done rounding, so I need a refresher course.

Thank you in advance for your help in this matter.

Recently I have heard mathematicians and statisticians comparing the various conventions. Both the conventions you mentioned came up.

However, if you think about it, there is .5 is the marginal middle point. If you are adding, and always rounded up, the errors would accumulate. If you always rounded down, they would always accumulate.

So the next step is some way to balance up and down to try to keep the errors down.

Here are two conventions I have heard about:

• old chemistry tradition:
    -- up one time, down the next, alternating.
• another statistical convention (I believe):
    -- up if the previous digit is even, down if it is odd.
        E.g. 8.25 would go to 8.3, 8.15 would go to 8.1.

If you are familiar with some of the studies of what digits ACTUALLY occur in practice ( something the tax people use to detect whether figures are made-up or are likely to be real), then I suspect that there IS a slight bias to the rule (b) since not all digits occure equally often. If the number is long enough, that is probably ok. If you are looking at the FIRST digit, it is pretty clear that 1 occurs far more often than 9. Going from 1000 to 2000, say in the stock market, is a 100% increase. Going from 9000 to 10,000 is a 11% increase!

Hopefully, some other responders can illustrate other options and conventions. There is a good reason you had this question! The answer is not 'logical' but conventional. As I read recently, if you have to remember, you are not DOING mathematics!

Walter Whiteley

I can add one convention to Walter's list. I know a statistician who uses a random number generator to decide whether to round up or down. A simple process would be to toss a coin, if it comes up heads round up, if tails round down.

Walter's point about errors accumulating is very important. When performing addition or subtraction always keep at least one more digit than you want in the final answer and then round to the correct number of digits just once, when you record the final answer.