Chapter 6.6, Problem 16WE

To determine

To write the given decimal as a common fraction in lowest terms.

Answer to Problem 16WE

  $0.\overline{5}=\frac{5}{9}$

Explanation of Solution

Given information :

Given number is $0.\overline{5}$ .

The given number has repeated decimal digits. We know $0.\overline{5}=\mathrm{0.555...}$

Now to convert this in fraction let us assume the number as $x$

Now $x=\mathrm{0.555...}$ (Equation 1)

Multiply by 10 on both sides we get,

  $10x=\mathrm{5.555....}$ (Equation 2)

Now we subtract equation 1 from equation 2 we get,

  $\begin{array}{l}10x-x=\mathrm{5.555...}-\mathrm{0.555...}\\ 9x=5\\ x=\frac{5}{9}\end{array}$

Hence we get the value $0.\overline{5}=\frac{5}{9}$