Denominator of 2, 4, or 5 to a Decimal

Definition

Proper fractions, are fractions where the numerator is smaller than the denominator. For example: 23,49,1113 are some proper fractions.

Some proper fractions have 2, 4 or 5 as their denominators.

There are certain shortcut methods for converting proper fractions with 2, 4 or 5 as denominators into decimals.

Rules for converting proper fractions with 2, 4 or 5 as denominators into decimals.

• At first, we write an equivalent fraction of given proper fraction with a denominator which is a power of ten.
• We then shift the decimal to as many places to the left as there are number of zeros after 1 in the denominator.

Example 1

Convert 12 into a decimal.

Solution

Step 1:

12 is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

Here, we write an equivalent fraction of 12 with a denominator 10.

12=(1×5)(2×5)=510

Step 3:

Shifting the decimal one place to the left we get

510=5.010=0.5

Step 4:

So, 12=0.5

Example 2

Convert 34 into a decimal.

Solution

Step 1:

34 is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

We write an equivalent fraction of 34 with a denominator 100.

34=(3×25)(4×25)=75100

Step 3:

Shifting the decimal two places to the left we get

75100=75.0100=0.75

Step 4:

So, 34=0.75

Example 3

Convert 25 into a decimal.

Solution

Step 1:

25 is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

We write an equivalent fraction of 25 with a denominator 10.

25=(2×2)(5×2)=410

Step 3:

Shifting the decimal one place to the left we get

410=4.010=0.4

Step 4:

So, 25=0.4