Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{\frac{9}{27}}$
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}$

(N/A) $(i)$ $\sqrt{\frac{9}{27}} = \sqrt{\frac{1}{3}} = \frac{1}{\sqrt{3}}$. Since $\sqrt{3}$ is an irrational number,the quotient of a rational number $(1)$ and an irrational number $(\sqrt{3})$ is an irrational number.
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}} = \sqrt{\frac{28}{343}} = \sqrt{\frac{4 \times 7}{49 \times 7}} = \sqrt{\frac{4}{49}} = \frac{2}{7}$. Since $\frac{2}{7}$ is in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$,it is a rational number.