Write the decimal expansion of $\frac{1}{7}$. Hence, write the decimal expansions of $\frac{2}{7},\frac{3}{7}, \frac{4}{7}, \frac{5}{7} \text{and} \frac{6}{7}$.

Express the following number in the form $\frac{p}{q}$, where $p$ and $q$ are both integers and $q\ne 0$.

$0.\overline{3}$

Express the following number in the form $\frac{p}{q}$, where $p$ and $q$ are both integers and $q\ne 0$.

$5.\overline{2}$

Express the following number in the form $\frac{p}{q}$, where $p$ and $q$ are both integers and $q\ne 0$.

$0.404040...$

Express the following number in the form $\frac{p}{q}$, where $p$ and $q$ are both integers and $q\ne 0$.

$0.4\overline{7}$

Express the following number in the form $\frac{p}{q}$, where $p$ and $q$ are both integers and $q\ne 0$.

$0.1\overline{34}$

Express the following number in the form $\frac{p}{q}$, where $p$ and $q$ are both integers and $q\ne 0$.

$0.\overline{001}$

Classify the following number as rational or irrational.

$\sqrt{23}$

Classify the following number as rational or irrational:

$\sqrt{225}$