Why do we generally round 5's up instead of down?

Question

As an example, the number 15, rounded to the nearest tens, rounds to 20. I understand it's arbitrary, as 10 and 20 are equidistant from 15, I just wonder if there's any discernible logic behind the convention of rounding up. Even something like, 'It just feels more natural', would probably satisfy me. Just had to ask :)

Answer 1

For small numbers like $15$, it may feel closer to $20$. We have a certain (vague) logarithmic appreciation of numbers, so $15$ feels farther from $10$ than from $20$. As the numbers get larger, this becomes less important. Even $25$ doesn't feel to me much closer to $30$ than $20$. But you have to do something. Sometimes you round to evens, which has the advantage of not accumulating errors if you add up a lot of them.

Answer 2

It isn't always. A popular rounding method called banker's rounding rounds 15 to 20 but 45 to 40.

But one reason it might be rounded that way is that round(x) is often implemented as $\lfloor x+1/2\rfloor.$

Answer 3

Wikipedia does have a nice article on this problem. Hope it helps in any way.

Answer 4

I guess, the convention is , for $.5$, you move to even one.

Answer 5

Another reason could be that if you only look at the first $k$ decimals after the point and it ends with $5$, then the most likely outcome is that what goes to the right isn't all zeros.

Answer 6

I randomly realized that 1.5 is no further away from 1 than it is from 2 just now and was compelled to ask the same question. After reading some of the answers, it occurred to me that the convention, it seems to reason, arises purely for the sake convenience. You see, necessarily, the more digits a decimal has, the larger the value is or becomes (if we of course disregard trailing 0s). For example, no matter how many digits you append to the end of 1.5 (e.g. 1.54, then 1.549, then 1.5491, and so forth), the value always increases and never decreases. Therefore, rounding up is the most convenient way to approximate without further compromising integrity or precision. In other words, doing it this way ensures we can disregard the greatest and or consider the least amount of information while maintaining a stable level of precision.