Question

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

• A. $\frac{27161}{999}$
• B. $\frac{27}{99}$
• C. $\frac{27161}{9900}$
• D. $\frac{27161}{9000}$

Answer 1

The correct option is C

$\frac{27161}{9900}$

The rational form of any number is of the form $\frac{p}{q},p,q$ are integer and $q\ne 0$

Let $x=2.74\overline{35}=2.743535...$ and $100x=274.3535...$ and $10000x=27435.3535...$

$$\begin{gathered} 10000x-100x=27435.3535...-274.3535... \\ 9900x=27161 \\ x=\frac{27161}{9900} \end{gathered}$$ [For terminating the repeating part to the right of the decimal point]

Therefore, the rational form of $2.74\overline{35}$ is $\frac{27161}{9900}.$

Hence, option (C) is correct.