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### Question

What is 0.67676767...?

**A**

$67/99$.

**B**

$68/99$.

**C**

$67/100$.

**D**

$67/101$.

**Soln.**

**Ans: a**

0.67676767... is same as $0.\ov 67$. Let y = $0.\ov 67$. Multiply by 100, 100y = 67 + $0.\ov 67$ which is same as 67 + y. So 99y = 67, ⇒ y = $67/99$. So answer = ${67/99}$.