Question 86

The rational numbers with recurring decimal expansion $$0.\overline{12}$$ is

Solution

Let a = $$0.\overline{12}$$ ........(1)

$$\Rightarrow$$ 100a = $$12.\overline{12}$$ ........(2)

Solving equation(2) - equation(1)

99a = 12

$$\Rightarrow$$ a = $$\frac{12}{99}$$

$$\Rightarrow$$ a = $$\frac{4}{33}$$

$$\Rightarrow$$ $$0.\overline{12}$$ = $$\frac{4}{33}$$

Hence, the correct answer is Option D

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