You can make sense of a percentage of natural numbers with the concept of natural density: https://en.wikipedia.org/wiki/Natural_density

The natural density of a set is the limit as N goes to infinity of the proportion of the numbers up to N which are in the set.

For instance the natural density of primes, squares and cubes is 0 and the natural density of even numbers is 1/2. But all these sets are infinite so the same cardinality.