Decimal $0.\overline{3} = 0.333...$ as a fraction is

Decimal $0.\overline{3} = 0.333...$ as a fraction is
  1. $\dfrac{1}{3}$
  2. $\dfrac{3}{10}$
  3. $\dfrac{33}{100}$
  4. $\dfrac{1}{30}$

Solution

Let $x = 0.\overline{3}$. Then $10x = 3.\overline{3}$. Subtract: $9x = 3 \Rightarrow x = \dfrac{1}{3}$.

Asked in: MH-SSC-9

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