What's the opposite of a "round number"?
Your presumed definition of a 'round number' is only partly correct. Consider this:
1000 is a "rounder" number than 1024.
Also:
1020 is a "rounder" number than 1024.
However,
1000 is a "rounder" number than 1020.
In other words, 1000 and 1020 are both obtained by 'rounding' off 1024. Therefore, a number's 'roundness' is based on two factors: that which it is rounding and the degree to which it is rounding off.
A 'rounded-off' number is the result of an original number being operated upon. The original number cannot be 'defined' (or named) in terms of what it may be rounded into from time to time.
In absolute terms, (see above) one could call such a number a
sharp number
n. A precise or unrounded number.
… Round numbers have a salient conceptual basis (e.g., 10 years are a decade). Sharp numbers do not (e.g., 7 years). Estimates tend to be expressed with round numbers. An experiment is described that examines whether consumers make the false assumption that claims using sharp numbers are less likely to be estimates (i.e., are more factual) than those using round numbers and, if so, whether this makes sharp-number claims more believable. The results demonstrate that such assumptions do occur, particularly for those consumers considered to be advertising skeptics. —Robert M. Schindler, Richard F. Yalch, "It Seems Factual, But Is It? Effects of Using Sharp Versus Round Numbers in Advertising Claims," Association for Consumer Research, October 1, 2005
The opposite of a round number is an exact number. The meaning is literal. When someone talks about round numbers, they usually are implying they are not exact.
You may also be familiar with the terms precise number and accurate number. A common expression is "accurate to X digits", meaning only X digits are correct, and the other digits have been "rounded". "Precise" can be used in a similar way. In other words, a rounded number can be accurate (or precise) with some describable error. It may be accurate or precise (to within some specified of stated error), but it's still a round number. It's not exact.