We have
0,ababab = $\frac{ab}{100 - 1}$ = $\frac{ab}{99}$
If $\frac{ab}{99}$ is an integer,
=> 1 : $\frac{ab}{99}$ = $\frac{99}{ab}$
=> ab is a divisor of 99 = {1;3;9;11;33;99}
If ab = 1: => $\frac{1}{99}$ = 0,0101010101...
=> Inverse number: = 1 : $\frac{1}{99}$ = 99 (satisfy)
If ab = 3 => $\frac{3}{99}$ = $\frac{1}{3}$ = 0,0303030303...
=> Inverse number: = 1 : $\frac{1}{33}$ = 33 (satisfy)
If ab = 9 => $\frac{9}{99}$ = $\frac{1}{11}$ = 0,0909090909...
=> => Inverse number: = 1 : $\frac{1}{33}$ = 11 (satisfy)
If ab = 11 =>$\frac{11}{99}$ = $\frac{1}{9}$ = 0,111111111111.....
(not satisfy because a and b different digits.)
If ab = 33 =>$\frac{33}{99}$ = $\frac{1}{3}$ = 0,333333333333......
(not satisfy because a and b different digits.)
If ab = 99 => $\frac{99}{99}$ = 1 (not satisfy because a and b different digits.)
So ab = {1;3;9}
=> There're 3 values of that number.
