Converting a Fraction to a Repeating Decimal - Advanced

Introduction

In this lesson, we are considering converting improper fractions into repeating decimals.

Example 1

Convert $\frac{11}{6}$ into a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Step 1:

At first, we set up the fraction as a long division problem, dividing 11 by 6

Step 2:

We find that on long division $\frac{11}{6} = 1.8333...$

Step 3:

The digit 3 keeps on repeating, so we write a bar over 3.

Step 4:

So, $\frac{11}{6} = 1.\overline{83}$

Example 2

Convert $\frac{73}{66}$ into a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Step 1:

At first, we set up the fraction as a long division problem, dividing 73 by 66

Step 2:

We find that $\frac{73}{66}$ on long division = 1.1060606...

Step 3:

The group of digits 06 keep on repeating, so we write a bar over them.

Step 4:

So, $\frac{73}{66} = 1.10606.. = 1.1\overline{06}$

Example 3

Convert $\frac{113}{105}$ into a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Step 1:

At first, we set up the fraction as a long division problem, dividing 113 by 105.

Step 2:

We find that $\frac{113}{105}$ on long division = 1.10761904761904...

Step 3:

The group of digits 761904 keep on repeating, we write a bar over these.

Step 4:

So, $\frac{113}{105} = 1.10761904761904... = 1.10\overline{761904}$