Question
Express the following recurring decimals as rational numbers.
$2 . \overline{4}$
$2 . \overline{4}$
The terms 0.4, 0.04, 0.004,… are in G.P.
$\therefore a=0.4, r=\frac{0.07}{0.7}=0.1,|r|=10.11<1$
∴ Sum to infinity exists.
∴ Sum to infinity
$\begin{aligned}=2+\frac{a}{1-r} & =2+\frac{0.4}{1-0.1} \\ & =2+\frac{0.4}{0.9} \\ & =2+\frac{4}{9}=\frac{22}{9}\end{aligned}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$(a-b)^{-1 / 4}$