Converting a Fraction to a Terminating Decimal – Basic

Definition

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.

25=0.4;24=0.75;2516=1.562525=0.4;24=0.75;2516=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.Example 1

Convert 3434 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 34=0.7534=0.75 which is a terminating decimal.

OR

Step 3:

We write an equivalent fraction of 3434 with a denominator 100.

34=(3×25)(4×25)=7510034=(3×25)(4×25)=75100

Step 4:

Shifting the decimal two places to the left we get

75100=75.0100=0.7575100=75.0100=0.75

Step 5:

So, 34=0.7534=0.75 which again is a terminating decimal.Example 2

Convert 23252325 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 2325=0.922325=0.92 which is a terminating decimal

OR

Step 3:

We write an equivalent fraction of 23252325 with a denominator 100.

2325=(23×4)(25×4)=921002325=(23×4)(25×4)=92100

Step 4:

Shifting the decimal two places to the left we get

92100=92.0100=0.9292100=92.0100=0.92

Step 5:

So, 2325=0.92