For each question,select the proper option from the four options given to make the statement true: $0.\overline{3} = \dots$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.2$

You know that $\frac{1}{7} = 0.\overline{142857}$. Can you predict what the decimal expansions of $\frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}$ are,without actually doing the long division? If so,how?

Express the following in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0.\overline{6}$
$(ii)$ $0.4\overline{7}$
$(iii)$ $0.\overline{001}$

Express $0.\overline{4}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Is $0.3\overline{7}$ a rational number or an irrational number?