Question

Write the decimal as a fraction or mixed number.

$\mathbf{-}\mathbf{9}\mathbf{.}\overline{\mathbf{6}}$

Short answer

The fraction is $-\frac{29}{3}$.

Step-by-step solution

Step 1. Given information

Consider, the decimal $-9.\overline{6}$ provided in question.

Step 2. Calculation

Consider$-9·\overline{6}=-9-0·\overline{6}$

But $-0·\overline{6}=\frac{-6}{9}$

Therefore,

$\begin{array}{c}-9\cdot \overline{6}=-9+\left(\frac{-6}{9}\right)\\ =\frac{(-9\times 9)-6}{9}\\ =\frac{-87}{9}\\ =\frac{-29}{3}\end{array}$

Thus, the fraction number that can be formed is$\frac{-29}{3}$.