Write three numbers whose decimal expansions are non-terminating non-recurring.

Is zero a rational number ? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$ ?

Classify the following numbers as rational or irrational :

$(i)$ $\sqrt{23}$

$(ii)$ $\sqrt{225}$

$(iii)$ $0.3796$

$(iv)$ $7.478478 \ldots$

$(v)$ $1.101001000100001 \ldots$

Express $0.99999 \ldots$ in the form $\frac{p}{q}$. Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense.

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

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

$(i)$ $0 . \overline{6}$

$(ii)$ $0 . 4\overline{7}$

$(iii)$ $0 . \overline{001}$