One distinction is that rational numbers are countably infinite. But irrational numbers are uncountably infinite. They have the same infinite density in every numerical range, is one way to think of it. An irrational number is represented mathematically as an infinite string of numbers. Since it is irrational, it does not have an exact representation in any number system, so it would take an infinite sequence of digits to exactly describe it. This is a distinction from rational numbers, where we know that 0.3... is exactly 1/3, and so on. If a number doesn't have an exact representation, it repeats. Irrational numbers do not, by definition.

Take that infinite set of irrational numbers in the [0,1) and multiply it by 0.1 (just for the convenience, of thinking of the string of digits, in decimal). Now, you have that same infinity in [0,0.1). And add 0.1 offsets, you have that same infinity in the range of [0.1, 0.2), [0.2, 0.3). Now, the use of decimal is arbitrary, the same idea applies for any scalar or number base system.