In elementary school, I learned that the round numbers ended with 0. As I progressed, I came to realize that this was equivalent to saying that round numbers are integer-multiples of 10.

Now that you’re asking the question, I would generalize that, so that round numbers are multiples of the base.

In binary (converted to decimal), that would be 2, 4, 6, 8, …

In octal (converted to decimal)l, that would be 8, 16, 24, 32, …

… and so on.

I also have no problem with negative round numbers.

It strikes me that 0 seems to be a canonical round number in that it’s a round number regardless of base.

I wouldn’t object if you were to say that round numbers are integer powers of the base (10, 100, 1000, … for decimal). If your definition doesn’t include 0, then I’ll expect a good explanation for why not.

But, truth be told, I could learn to live with any definition I can wrap my head around, as long as I can use my elementary school definition in polite company. :)