• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q17.

Expert-verified Found in: Page 224 ### 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.$\mathbf{2}\mathbf{.}\overline{\mathbf{6}}$

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

See the step by step solution

## Step 1. Given information

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

## Step 2. Calculation

To evaluate fraction number of decimal $2.\overline{6}$, 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:

$\begin{array}{c}x=2.\overline{6}\\ =2.66...\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}equation(1)\hspace{0.17em}}\end{array}$

By multiplying 10 each sides.

$\text{10}x=26.66... \text{equation(2)}$

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

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

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

$\begin{array}{c}\frac{24}{9}=\frac{8}{3}\\ =2.\overline{6}\\ =2\frac{2}{3}\end{array}$

Hence,

$2\frac{2}{3}$ is the mixed number of decimal $2.\overline{6}$ ### Want to see more solutions like these? 