How many rational numbers are there between any two distinct rationals?

This is the density property of rational numbers. Between any two distinct rationals a and b, there are infinitely many other rationals. One way to construct: keep taking averages (a+b)/2, then average each new value with one of a, b, and so on — every step gives a new rational. This is why rationals 'fill' the number line densely (though irrationals fill the remaining gaps).