## Work Time

# Repeating Decimals

To indicate that a decimal repeats forever in a specific pattern, you write a bar over the repeating digits.

For example, $\frac{6}{11}=0.54545454545\dots $. You can write this decimal as $0.\overline{54}$. The use of a line to show the repeating digits in a decimal is called *bar notation*.

Write each of these fractions in decimal form using bar notation.

- $\frac{1}{3}$
- $\frac{2}{3}$
- $\frac{11}{12}$
- $\frac{3}{11}$

# Challenge Problem

It is easy to change a terminating decimal to a fraction; for example, $0.09=\frac{9}{100}$ and $3.2=\frac{32}{10}$.

Changing a repeating decimal to a fraction is trickier. The steps that follow describe a method for changing the repeating decimal $0.\overline{12}$ to a fraction.

** • Use this method to change $0.\overline{7}$ to a fraction.**