I remember seeing on some cooking show that you are always supposed to cut
off one end of the onion if you were not going to use all of it. If you
didn't, it would continue to grow. I can't remember if they said the root
or top end. I think they said root. But... I almost always cut off both
ends and put the rest in the fridge. I would only leave the peel on if I
were in a super hurry to get a piece of onion. I have done this when making
a sandwich in a hurry. Wash, cut a slice, just removing the peel from the
slice then putting the onion in a plastic bag in the fridge to deal with
later.

But lately, I cut off both ends, peel and put the rest of the onion in a
plastic bag but... The onion continues to seem to grow from the top end.
It doesn't form a green sprout but pushes up from the middle until the
middle is sticking up. Makes it a tad hard to get good slices but is not a
problem for chunks or dices.