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Expert-verified Found in: Page 226 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Write $0.\overline{475}$ as a fraction. Describe the steps you take to write the fraction.

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

See the step by step solution

## Step 1. Given information

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

## Step 2. Calculation

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

$x=0.475475475$ …… (1)

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

Multiply equation (1) by 1000 on both sides,

$1000x=475.475475.....$ …… (2)

Subtract equation (1) from equation (2),

$\left(1000x=475.475475...\right)-\left(x=0.475475...\right)$

$\begin{array}{c}1000x-x=\left(475.475475.....\right)+\left(0.475475475.....\right)\\ 999x=475\\ x=\frac{475}{999}\end{array}$

Thus, the fraction number that can be formed is $\frac{475}{999}$. ### Want to see more solutions like these? 