Question

Convert into fraction $x=0.\overline{6}$

Answer 1

$x=0.\overline{6}$

$x=\mathrm{0.666666..............}$

$10x=10\times \mathrm{0.666666............}$

$10x=\mathrm{6.666666............}$

$10x=6+\mathrm{0.666666.............}$

$10x=6+0.\overline{6}$

$10x=6+x$

$10-x=6$

$9x=6$

$x=\frac{6}{9}$

$x=\frac{2}{3}$