Simplify the following.

​$$0.\overline{06} \times 8.\overline{3}$$​​

Correct option is C

Given:

$$0.\overline{06} \times 8.\overline{3}$$​

Let x = 0.060606..

100x = 6.0606…

100x -x = 6.0606… - 0.0606..

99x = 6

​$$x =\frac{6}{99} =\frac{2}{33}$$​​

Let y = 8.3333..

10y = 83.3333..

10y-y = 83.333.. -8.333..

9y= 75

​$$y= \frac{75}{9} = \frac{25}{3}$$​​

​$$0.\overline{06} \times 8.\overline{3}$$​​

​$$\frac{2}{33} \times \frac{25}{3}$$​​

​$$=\frac{50}{99}= 0.505050 = 0.\overline{50}$$​​