We need to form numbers of the type $0.XY$, where X and Y are distinct non-zero digits. The digits X and Y must be selected from the set of digits 1 to 9.

There are 9 options for the digit X (since it can be any digit from 1 to 9). Once X is chosen, there are 8 remaining options for the digit Y (since Y must be distinct from X).

Thus, the total number of ways to arrange X and Y is: $9 \times 8 = 72$

Hence, the correct answer is $72$.