[tex]5.38=5+0.38=5+\dfrac{38}{100}=5+\dfrac{38:2}{100:2}=5+\dfrac{19}{50}=\boxed{5\frac{19}{50}}[/tex]
[tex]x=0.474747...\ \ \ \ |multiply\ both\ sides\ by\ 100\\\\100x=47.474747...\\\\100x-x=47.474747...-0.474747...\\\\99x=47\ \ \ \ \ \ |divide\ both\ sids\ by\ 99\\\\x=\dfrac{47}{99}\\\\\boxed{0.474747...=\frac{47}{99}}[/tex]
