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.
$2 . \bar{6}$

$2 \frac{2}{3}$ is the fraction number of decimal $2 . \bar{6}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Consider, the decimal $2 . \bar{6}$ provided in question

Step 2. Calculation

To evaluate fraction number of decimal $2 . \bar{6}$ , it is needed to remove the bar as here one digit is repeating so multiply the number by 10

Therefore, the fraction number obtained as follows:

$\begin{matrix} x = 2. \bar{6} \\ = 2.66... equation(1) \end{matrix}$

By multiplying 10 each sides.

$10 x = 26.66 . . . equation(2)$

Subtract equation (1) from the equation (2).

$\begin{matrix} 10 x - x = 26.66... - 2.66... \\ 9 x = 24 \\ x = \frac{24}{9} \end{matrix}$

Simplify the fraction into mixed fraction and in decimal as follows:

$\begin{matrix} \frac{24}{9} = \frac{8}{3} \\ = 2. \bar{6} \\ = 2 \frac{2}{3} \end{matrix}$

Hence,

$2 \frac{2}{3}$ is the mixed number of decimal $2 . \bar{6}$

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