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Q75.

Expert-verified

Pre-algebra

Found in: Page 226

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 $0 . \bar{475}$ as a fraction. Describe the steps you take to write the fraction.

The fraction number of $0 . \bar{475}$ is $\frac{475}{999}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

The decimal number is $0 . \bar{475}$ .

Step 2. Calculation

Let $x = 0 . \bar{475}$

$x = 0.475475475$ …… (1)

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

Multiply equation (1) by 1000 on both sides,

$1000 x = 475.475475 . . . . .$ …… (2)

Subtract equation (1) from equation (2),

$(1000 x = 475 . 475475...) - (x = 0 . 475475...)$

$\begin{matrix} 1000 x - x = (475 . 475475.....) + (0 . 475475475.....) \\ 999 x = 475 \\ x = \frac{475}{999} \end{matrix}$

Thus, the fraction number that can be formed is $\frac{475}{999}$ .

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