Converting a Proper Fraction With a 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…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 1212 into a decimal.

Solution

Step 1:

1212 is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

Here, we write an equivalent fraction of 1212 with a denominator 10.

12=(1×5)(2×5)=51012=(1×5)(2×5)=510

Step 3:

Shifting the decimal one place to the left we get

510=5.010=0.5510=5.010=0.5

Step 4:

So, 12=0.512=0.5Example 2

Convert 3434 into a decimal.

Solution

Step 1:

3434 is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

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

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

Step 3:

Shifting the decimal two places to the left we get

75100=75.0100=0.7575100=75.0100=0.75

Step 4:

So, 34=0.7534=0.75Example 3

Convert 2525 into a decimal.

Solution

Step 1:

2525 is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

We write an equivalent fraction of 2525 with a denominator 10.

25=(2×2)(5×2)=41025=(2×2)(5×2)=410

Step 3:

Shifting the decimal one place to the left we get

410=4.010=0.4410=4.010=0.4

Step 4:

So, 25=0.4