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Q51.

Expert-verified
Found in: Page 225

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Write the decimal as a fraction or mixed number.$\mathbf{-}\mathbf{0}\mathbf{.}\overline{\mathbf{4}}$

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

See the step by step solution

## Step 1. Given information

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

## Step 2. Calculation

Let $x=-0×\overline{4}$

$x=-0·4444.....$ …… (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),

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

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

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