Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
There are infinite rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$
$\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}$
$\frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}$
Therefore, $5$ rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ (i.e. $\frac{18}{30}$ $ \frac{24}{30})$ are
$\frac{19}{30}, \,\frac{20}{30},\, \frac{21}{30}, \,\frac{22}{30},\, \frac{23}{30}$
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Express the following in the form $\frac {p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0 . \overline{6}$
$(ii)$ $0 . 4\overline{7}$
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$(ii)$ $0 . 4\overline{7}$
$(iii)$ $0 . \overline{001}$