Question

The sum of $0.\overline{6}$ and $0.\overline{7}$ is :-

• A. $1.\overline{3}$
• B. $1.3$
• C. $1.\overline{4}$
• D. an irrational number

Answer 1

The correct option is C $1.\overline{4}$

$x=0.\overline{6}$

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

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

$10x=6+x$

$9x=6$

$x=\frac{6}{9}=\frac{2}{3}$

$y=0.\overline{7}$

$10y=7.\overline{7}$

$10y=7+.\overline{7}$

$10y=7+y$

$9y=7$

$y=\frac{7}{9}$

$y+x=\frac{7}{9}+\frac{2}{3}$

$=\frac{7+6}{9}=\frac{13}{9}$

$=1.444$

$=1.\overline{4}$.