Enumerable means countable. Subset of countable set is countable. All countably infinite sets are the same cardinality as each other.

Is enumerable same as countable?

Yes. All subsets of the natural numbers are countable but not all of them are enumerable.

Are rationals countable?

The set of all rationals in [0, 1] is countable. ... Clearly, we can define a bijection from Q ∩ [0, 1] → N where each rational number is mapped to its index in the above set. Thus the set of all rational numbers in [0, 1] is countably infinite and thus countable.