Find the fraction form of 0.666....

Correct option is C

Given:

The repeating decimal is $$0.66666..$$​​

Solution:
Let x$$= 0.6666....$$​​
Multiply both sides by 10:

​$$10x = 6.6666....$$​

Now subtract the original equation from the new equation:

​$$10x - x = 6.6666\ldots - 0.6666\ldots$$​

9x = 6

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

Alternate Method:

Concept Used:

​$$0.\bar {a}=\frac{a}9$$

Solution:

$$0.\bar 6=\frac 69=\frac 23$$​

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