Chapter 11.6, Problem 17WE

To determine

To calculate:

Given repeating decimal as a common fraction.

Answer to Problem 17WE

Fraction of $0.3333$ is $\frac{32.9}{99}$ .

Explanation of Solution

Give information:

  $0.3333$

Calculation:

Given is $0.3333$ ,

Let $x=\mathrm{0.3333...}\left(i\right)$

S o multiply both sides by $100$

  $\begin{array}{l}100.x=\left(100\right)0.3333\\ 100x=33.33\end{array}$

now subtract above equation with eq. $\left(i\right)$

  $\begin{array}{l}100x-x=\mathrm{33.33....}-\mathrm{0.3333....}\\ 99x=32.9\end{array}$

Divide both sides by $99$

  $\begin{array}{l}\frac{99x}{99}=\frac{32.9}{99}\\ x=\frac{32.9}{99}\end{array}$

Thus, fraction of $0.3333$ is $\frac{32.9}{99}$ .