Question

Write the decimal as a fraction or mixed number.

$\mathbf{-}\mathbf{0}\mathbf{.}\overline{\mathbf{4}}$

Short answer

The fraction is $-\frac{4}{9}$.

Step-by-step solution

Step 1. Given information

Consider, the decimal $-0.\overline{4}$ provided in question

Step 2. Calculation 

Let $x=-0\times \overline{4}$

$x=-0·4444.....$ …… (1)

Clearly, 4 is the only digit which is repeating in equation (1)

Multiply equation (1) by 10 on both sides,

$10x=-4·4444.....$ …… (2)

Subtract equation (1) from equation (2),

$\begin{array}{c}10x-x=(-4\cdot \mathrm{4444...})-(-0\cdot \mathrm{4444...})\\ 9x=-4\\ x=\frac{-4}{9}\end{array}$

Thus, the fraction number that can be formed is $\frac{-4}{9}$.