Question

Write the repeating decimal as a fraction or a mixed number $-1.\overline{7}$.

Answer 1

Given number: $-1.\overline{7}$.

Let $\mathrm{x}=-1.\overline{7}$

$\Rightarrow \mathrm{x}=-1.777...$ …(i)

Multiply by $10$ both sides

$\Rightarrow 10\times \mathrm{x}=10\times -1.777...$

$\Rightarrow 10\mathrm{x}=-17.777...$ …(ii)

Subtract equation (i) from equation (ii),

$$\begin{gathered} \Rightarrow 10\mathrm{x}-\mathrm{x}=-17.777...-(-1.777...) \\ \Rightarrow 9x=-17.777...+1.777... \\ \Rightarrow 9\mathrm{x}=-16 \\ \Rightarrow \mathrm{x}=-\frac{16}{9} \end{gathered}$$

Hence, the fraction form of the given decimal number is$-\frac{16}{9}$.