# 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.

$\frac{1}{2} = \frac{\left ( 1\times 5 \right )}{\left ( 2\times 5 \right )} = \frac{5}{10}$

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.

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

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.

$\frac{2}{5} = \frac{\left ( 2\times 2 \right )}{\left ( 5\times 2 \right )} = \frac{4}{10}$

Step 3:

Shifting the decimal one place to the left we get

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

Step 4:

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