Converting a Fraction to a Terminating Decimal - Basic

A terminating decimal is a decimal that ends. In other words, a terminating decimal doesn't keep going. It has a finite number of digits after the decimal point.

$\frac{2}{5} = 0.4;\: \frac{2}{4} = 0.75;\: \frac{25}{16} = 1.5625$

In the examples shown above, we have few fractions expressed as decimals. Notice that these decimals have a finite number of digits after the decimal point. So, these are terminating decimals.

Rule to convert a fraction to a terminating decimal

• To convert a fraction into a terminating decimal, the method is to set up the fraction as a long division problem to get the answer.

Here we are converting proper fractions into terminating decimals.

Convert $\frac{3}{4}$ into a decimal.

Solution

Step 1:

At first, we set up the fraction as a long division problem, dividing 3 by 4

Step 2:

We find that on long division $\frac{3}{4} = 0.75$ which is a terminating decimal.

OR

Step 3:

We write an equivalent fraction of $\frac{3}{4}$ with a denominator 100.

$\frac{3}{4} = \frac{\left ( 3 \times 25 \right )}{\left ( 4 \times 25 \right )} = \frac{75}{100}$

Step 4:

Shifting the decimal two places to the left we get

$\frac{75}{100} = \frac{75.0}{100} = 0.75$

Step 5:

So, $\frac{3}{4} = 0.75$ which again is a terminating decimal.

Convert $\frac{23}{25}$ into a decimal.

Solution

Step 1:

At first, we can set up the fraction as a long division problem, dividing 23 by 25

Step 2:

We find that on long division $\frac{23}{25} = 0.92$ which is a terminating decimal

OR

Step 3:

We write an equivalent fraction of $\frac{23}{25}$ with a denominator 100.

$\frac{23}{25} = \frac{\left ( 23 \times 4 \right )}{\left ( 25 \times 4 \right )} = \frac{92}{100}$

Step 4:

Shifting the decimal two places to the left we get

$\frac{92}{100} = \frac{92.0}{100} = 0.92$

Step 5:

So, $\frac{23}{25} = 0.92$