Well we all know that between any two real numbers there is a rational. Mathematicians like to say that the rationals are dense in the real line... what this means is that any open set will contain some rational. So they are "everywhere" in the line, aren't they?
Well, it depends on what you mean by "everywhere".
One could argue that the rationals are pretty sparsely populated in the reals: I claim that you can cover the rationals by a set whose "length" is arbitrarily small. In other words, give me a string of any positive length, no matter how short, and I will be able to cover all the rationals with it!
Since the rationals are countable, I can run through them sequentially, one by one. Take the string, cut it in half, and cover the first rational with it. Then take what's left of the string, cut it in half, and use that to cover the 2nd rational. Continue in this fashion, taking what's left of the string, cutting it in half, and using that to cover the N-th rational.
When complete, all the rationals will be covered! So the rationals are dense but also "sparse"!