Evaluate $ \frac{2}{3}+0 . \overline{11} $.

Given :

\( \frac{2}{3}+0 . \overline{11} \).

To do :

We have to evaluate \( \frac{2}{3}+0 . \overline{11} \).

Solution :

$0. \overline{11}$

Let $x = 0.1111....$

Multiply both sides by 100.

$100x = 100(0.1111....)$

$100x = 11.1111.....$

Therefore,

$100x-x = 11.1111.... - 0.1111.....$

$99x = 11$

$x = \frac{11}{99}=\frac{1}{9}$

Therefore,

$\frac{2}{3}+0 . \overline{11}=\frac{2}{3}+\frac{1}{9}$

$=\frac{2\times3+1}{9}$

$=\frac{6+1}{9}$

$=\frac{7}{9}$

Hence, \( \frac{2}{3}+0 . \overline{11}=\frac{7}{9} \).

Tutorialspoint

Updated on: 10-Oct-2022

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