Converting a Proper Fraction With a Denominator of 2, 4, or 5 to a Decimal

Proper fractions, are fractions where the numerator is smaller than the denominator. For example: $frac{2}{3}, frac{4}{9}, frac{11}{13}…$ 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.

Convert $frac{1}{2}$ into a decimal.

Solution

Step 1:

$frac{1}{2}$ is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

Here, we write an equivalent fraction of $frac{1}{2}$ with a denominator 10.

$frac{1}{2} = frac{left ( 1 imes 5 ight )}{left ( 2 imes 5 ight )} = frac{5}{10}$

Step 3:

Shifting the decimal one place to the left we get

$frac{5}{10} = frac{5.0}{10} = 0.5$

Step 4:

So, $frac{1}{2} = 0.5$

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

Solution

Step 1:

$frac{3}{4}$ is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

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

$frac{3}{4} = frac{left ( 3 imes 25 ight )}{left ( 4 imes 25 ight )} = frac{75}{100}$

Step 3:

Shifting the decimal two places to the left we get

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

Step 4:

So, $frac{3}{4} = 0.75$

Convert $frac{2}{5}$ into a decimal.

Solution

Step 1:

$frac{2}{5}$ is a proper fraction of the type where the denominator is 2,4 or 5.

Step 2:

We write an equivalent fraction of $frac{2}{5}$ with a denominator 10.

$frac{2}{5} = frac{left ( 2 imes 2 ight )}{left ( 5 imes 2 ight )} = frac{4}{10}$

Step 3:

Shifting the decimal one place to the left we get

$frac{4}{10} = frac{4.0}{10} = 0.4$

Step 4:

So, $frac{2}{5} = 0.4$