please me on number theory

.030303  =   3/99

.033333= 1/30       can you take it from here??

we know that   $0.\overline{03}=3/99$ and $0.0\overline{3}=1/30$ so we have the equation $\dfrac{3/99}{1/30}=\dfrac{30}{99/3}=\dfrac{30}{33}=\dfrac{10}{11}$so our final answer is $\Huge{\boxed{\boxed{\boxed{\boxed{\dfrac{10}{11}}}}}}$