Write the decimal expansion of each of the following numbers and say what kind of decimal expansion each has:

$\begin{matrix} \text{(i)} & \dfrac{36}{100} \\[1.5em] \text{(ii)} & 4\dfrac{1}{8} \\[1.5em] \text{(iii)} & \dfrac{2}{9} \\[1.5em] \text{(iv)} & \dfrac{2}{11} \\[1.5em] \text{(v)} & \dfrac{3}{13} \\[1.5em] \text{(vi)} & \dfrac{329}{400} \\[1.5em] \end{matrix}$

$\text{(i) } \dfrac{36}{100}$

$\therefore \dfrac{36}{100} = 0.36$

Remainder becomes zero.

Decimal expansion of $\bold{\dfrac{36}{100}}$ is terminating.

$\text{(ii) } 4\dfrac{1}{8}$

$\therefore 4\dfrac{1}{8} = 4.125$

Remainder becomes zero.

Decimal expansion of $\bold{4\dfrac{1}{8}}$ is terminating.

$\text{(iii) } \dfrac{2}{9}$

$\therefore \dfrac{2}{9} = 0.2222….. = 0.\overline{2}$

Remainder is repeating.

Decimal expansion of $\bold{\dfrac{2}{9}}$ is non-terminating repeating.

$\text{(iv) } \dfrac{2}{11}$

$\therefore \dfrac{2}{11} = 0.1818….. = 0.\overline{18}$

Remainder is repeating.

Decimal expansion of $\bold{\dfrac{2}{11}}$ is non-terminating repeating.

$\text{(v) } \dfrac{3}{13}$

$\therefore \dfrac{3}{13} = 0.2307692307….. = 0.\overline{230769}$

Remainder is repeating.

Decimal expansion of $\bold{\dfrac{3}{13}}$ is non-terminating repeating.

$\text{(vi) } \dfrac{329}{400}$

$\therefore \dfrac{329}{400} = 0.8225$

Remainder becomes zero.

Decimal expansion of $\bold{\dfrac{329}{400}}$ is terminating.