Question

Add or subtract.

$\frac{11}{6}-0.\overline{27}$.

Answer 1

Step 1: Find the fraction form of $0.\overline{27}$

Given: $\frac{11}{6}-0.\overline{27}$

Let $\mathrm{x}=0.\overline{27}$

$\Rightarrow \mathrm{x}=0.272727...$ …(i)

Multiply by $100$ both sides

$\Rightarrow 100\times \mathrm{x}=100\times 0.272727...$

$\Rightarrow 100\mathrm{x}=27.272727...$ …(ii)

Subtract equation (i) from equation (ii)

$$\begin{gathered} \Rightarrow 100\mathrm{x}-\mathrm{x}=27.272727...-0.272727... \\ \Rightarrow 99\mathrm{x}=27 \\ \Rightarrow \mathrm{x}=\frac{27}{99} \\ \Rightarrow \mathrm{x}=\frac{3}{11} \end{gathered}$$

Hence, fraction form of $0.\overline{27}$ is $\frac{3}{11}$.

Step 2: Find $\frac{11}{6}-0.\overline{27}$.

Since, $0.\overline{27}=\frac{3}{11}$.

Now,

$$\begin{gathered} \frac{11}{6}-0.\overline{27} \\ =\frac{11}{6}-\frac{3}{11} \\ =\frac{121-18}{66} \\ =\frac{103}{66} \end{gathered}$$

Hence, $\frac{11}{6}-0.\overline{27}=\frac{103}{66}$.