Find the reciprocal of $.\overline{2} + .\overline{6}$ expressed as a decimal
Find the reciprocal of $$.\overline{2} + .\overline{6}$$ expressed as a decimal
$$\\0.\overline{2} = \dfrac{ 1 } {4.5 } \\\\
0.\overline{6} = \dfrac{ 1 } { 1.5 } \\\\$$
so wie have:
$$\small{\text{
$
\dfrac{1} { 0.\overline{2} + 0.\overline{6} }
= \dfrac{1} { \dfrac{ 1 } { 4.5 } + \dfrac{ 1 } { 1.5 } }
=\dfrac{1} { \dfrac{ 1.5+4.5 } { 1.5\cdot 4.5 } }
= \dfrac{ 1.5\cdot 4.5 }{ 1.5+4.5 }
=\dfrac{ 6.75 }{ 6 } = 1.125
$}}$$