Question

The rational form of $2.74\overline{35}$ is

• A. $\frac{27161}{9999}$
• B. $\frac{27}{99}$
• C. $\frac{27161}{9900}$
• D. $\frac{27161}{9000}$

Answer 1

Answer: (C)

$\frac{27161}{9900}$

Let $x=2.74\overline{35}$

As the bar is under two digits multiply with $100$

$100x=2.7435\times 100$

$100x=274.35$

Now, subtract with $x$ terms, we get

$99x=274.35-2.7435$

$99x=271.60$

$x=\frac{271.60}{99}$

$x=\frac{27160}{9900}$

Hence, this is the answer.