Question

Write the decimal as a fraction or a mixed number $2.0\overline{6}$.

Answer 1

Given number: $2.0\overline{6}$

Let $\mathrm{x}=2.0666\dots$

Multiply by $10$ on both the sides;

$\Rightarrow 10\times \mathrm{x}=10\times 2.0666\dots$

$\Rightarrow 10\mathrm{x}=20.666\dots$ …(i)

Again multiply by $10$ on both the sides;

$\Rightarrow 10\times 10\mathrm{x}=10\times 20.666\dots$

$\Rightarrow 100\mathrm{x}=206.666...$ …(ii)

Subtract equation (i) from equation (ii),

$$\begin{gathered} \Rightarrow 100\mathrm{x}-10\mathrm{x}=206.666...-20.666... \\ \Rightarrow 90\mathrm{x}=186 \\ \Rightarrow \mathrm{x}=\frac{186}{90} \\ \Rightarrow \mathrm{x}=\frac{93}{45} \end{gathered}$$

Hence, the fraction form of a given decimal number is $\frac{93}{45}$.