I think you mean b is not equal to 0.
We have that 11.424242... = 11 + 0.424242...
Now let x = 0.424242...
Then 100x = 42.424242...
Now 99x = 100x - x = 42 so 99x = 42 and therefore x = 42/99
Now we can simplify 42/99 to 14/33
Now combining this we get 11.424242... = 11 + 14/33
= 363/33 + 14/33 = 377/33
