Question

Express the following decimal in the form $\frac{p}{q}$:

$0.\overline{54}$

• A. $\frac{6}{111}$
• B. $\frac{60}{11}$
• C. $\frac{6}{11}$
• D. None of the above

Answer 1

Answer: (C)

$\frac{6}{11}$

Given,

$0.\overline{54}$

Let $x=0.544444$.....(1)

$100x=54$.........(2)

(2)-(1) gives,

$99x=54$

$\therefore x=\frac{6}{11}$