Divide $8 \sqrt{15}$ by $2 \sqrt{3}$.

Classify the following numbers as rational or irrational:
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$

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?

Recall,$\pi$ is defined as the ratio of the circumference (say $c$) of a circle to its diameter (say $d$). That is,$\pi = \frac{c}{d}$. This seems to contradict the fact that $\pi$ is irrational. How will you resolve this contradiction?

Find the decimal expansions of $\frac{10}{3}$,$\frac{7}{8}$ and $\frac{1}{7}$.

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$?