Convert 11.42424242 to a rational expression in the form a/b, where b=0

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