Well, [tex]11.42424242[/tex] is a rational expression already. Of course:
[tex]11.42424242 = 11+\dfrac{42424242}{10^8} = \dfrac{1142424242}{10^8}[/tex].
But maybe you mean [tex]11.\overline{42} = 11.4242\dots[/tex] So:
[tex]x = 11.\overline{42} \iff 100x = 1142.\overline{42} \iff 99x = 1131 \iff x = \frac{1131}{99} = \frac{377}{33}[/tex]
