Converting a Fraction to a Terminating Decimal - Advanced

We have learnt about terminating decimals in previous lesson. In this lesson we are considering converting improper fractions into terminating decimals.

Improper fractions are those fractions where the numerator is greater than the denominator. For example, $\frac{9}{8}$ is an improper fraction. The numerator 9 is greater than the denominator 8.

• To convert the improper fraction into a terminating decimal, we set up the fraction as a long division problem

• For example, dividing 9 by 8, we get $\frac{9}{8} = 1.125$, a terminating decimal.

Convert $\frac{13}{2}$ into a decimal.

Solution

Step 1:

First, we set up the fraction as a long division problem, dividing 13 by 2

We find that on long division $\frac{13}{2} = 6.5$

OR

Step 2:

We write an equivalent fraction of $\frac{13}{2}$ with a denominator 10.

$\frac{13}{2} = \frac{\left ( 13 \times 5 \right )}{\left ( 2 \times 5 \right )} = \frac{65}{10}$

Step 3:

Shifting the decimal one place to the left we get

$\frac{65}{10} = \frac{65.0}{10} = 6.5$

Step 4:

So, $\frac{13}{2} = 6.5$

Convert $\frac{29}{25}$ into a decimal.

Solution

Step 1:

At first, we set up the fraction as a long division problem, dividing 29 by 25

We find that on long division $\frac{29}{25} = 1.16$

OR

Step 2:

We write an equivalent fraction of $\frac{29}{25}$ with a denominator 100.

$\frac{29}{25} = \frac{\left ( 29 \times 4 \right )}{\left ( 25 \times 4 \right )} = \frac{116}{100}$

Step 3:

Shifting the decimal two places to the left we get

$\frac{116}{100} = \frac{116.0}{100} = 1.16$

Step 4:

So, $\frac{29}{25} = 1.16$