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Q51.

Expert-verified

Pre-algebra

Found in: Page 225

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

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

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

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

Step 2. Calculation

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

$x = - 0 \cdot 4444 . . . . .$ …… (1)

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

Multiply equation (1) by 10 on both sides,

$10 x = - 4 \cdot 4444 . . . . .$ …… (2)

Subtract equation (1) from equation (2),

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

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

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