Question

The value of $n=\mathrm{0.5757....}$ is equivalent to

• A. $\frac{9}{33}$
• B. $\frac{57}{99}$
• C. $\frac{19}{33}$
• D. None of the above

Answer 1

Answer: (B), (C)

The correct options are
B $\frac{57}{99}$
C $\frac{19}{33}$

Given,

$n=\mathrm{0.5757...}$ $...\left(1\right)$
On multiplying $100$ to both sides, we get:

$\Rightarrow 100n=\mathrm{57.5757....}$ $...\left(2\right)$

On subtractinf $\left(1\right)$ from $\left(2\right)$, we get:

$99n=57$

Hence, $n=\frac{57}{99}$

Or $n=\frac{19}{33}$

Hence, both option B and option C are correct.