Why, when rounding, do we round 5 up to 10?

Question

If we cut 10 in half, then we get 5. This means two 5s makes 10, meaning, 6, 7, 8, 9, and 10, are the remaining 5 numbers that make it up. So why do we round up 6 numbers? It's such a small thing but it annoys me so much.

Answer 1

$5$ is as close to $10$ as it is to $0$. So that doesn't decide the issue. But if you always round these borderline cases up, or you always round them down, then you increase the rate that rounding errors accumulate over a sequence of calculations. And if you alternate between rounding up and rounding down, as some stone-age computers did, you lose reproducibility of results. So computers these days generally use round to even: if a number is equally close to two rounding candidates, choose the even one. Loosely speaking, this strategy makes it more likely that rounding errors will cancel out in the long run.

Here you are rounding to a multiple of $10$, so the strategy is to round to the nearest even multiple of $10$. So $5$ will round down to $0$. I hope this makes you feel better :-)