In algebra, we deal a lot with sets of real numbers. Real numbers contain rational numbers, such as integers and the fractions, and all irrational numbers such as non terminating numbers and π a transcendental number. Writing a number in the decimal or fraction form is just a representation of it. A fraction represents a part of a whole number and decimal can be defined as a number containing decimal points. In some situation, it can be defined as a decimal point followed by a digit as a method to show values less than one. In fractions, we need to deal with the denominator, as it not easy to add or subtract unlike fractions. In such situations, we make use of decimal numbers.

## Decimal and Fractions

While comparing, the decimal having certain advantages than fractions:

- When two numbers are compared, it is easier to see which number is relatively greater(or lesser) in the decimal form rather than the fractional form.
**For example**it is easy to see that $1.54$ is greater than $1.36$ than to see $\frac{77}{50}$ is greater than $\frac{34}{25}$. - It is easy to calculate decimal numbers on a calculator as putting a fraction in some calculators is not possible.
- The decimal value can be written in the percentage form more easily than fractions.
**For example,**$0.35 = 35$% - It is totally compatible with the metric system of measurement.

### Solved Example

**Question:**Add $\frac{4}{5}$ and $ \frac{2}{10}$.

**Solution:**

In order to add fractions, the denominators must be same.

$\frac{4}{5}$ + $ \frac{2}{10}$ = $\frac{4}{5}\ast \frac{2}{2} + \frac{2}{10}$

= $\frac{8}{10} + \frac{2}{10}$

= $ \frac{8+2}{10} $

= $ \frac{10}{10} $

= $1$

Now in the decimal form:

$\frac{4}{5}$ = 0.8 and

$\frac{2}{10}$ = 0.2

So $\frac{4}{5} + \frac{2}{10}$ = 0.8 + 0.2 = 1.0 = 1

It is very clear that using the decimal format is more easy than using the fraction format in certain situations.

$\frac{4}{5}$ + $ \frac{2}{10}$ = $\frac{4}{5}\ast \frac{2}{2} + \frac{2}{10}$

= $\frac{8}{10} + \frac{2}{10}$

= $ \frac{8+2}{10} $

= $ \frac{10}{10} $

= $1$

Now in the decimal form:

$\frac{4}{5}$ = 0.8 and

$\frac{2}{10}$ = 0.2

So $\frac{4}{5} + \frac{2}{10}$ = 0.8 + 0.2 = 1.0 = 1

It is very clear that using the decimal format is more easy than using the fraction format in certain situations.

## How to Convert Fractions to Decimals

**divide the numerator by the denominator.**

### Solved Examples

**Question 1:**Convert $\frac{2}{5}$ to decimal.

**Solution:**

Here, the numerator = 2 is
less than the denominator = 5,

So we put a decimal in the quotient and take 20 for 2.

now, numerator = 20 is greater than the denominator = 5.

So lets check the multiples of 5. As $5*4 = 20$, the answer is $0.4$

=> $\frac{2}{5}$ = $0.4$.

So we put a decimal in the quotient and take 20 for 2.

now, numerator = 20 is greater than the denominator = 5.

So lets check the multiples of 5. As $5*4 = 20$, the answer is $0.4$

=> $\frac{2}{5}$ = $0.4$.

**Question 2:**Convert $\frac{3}{4}$ to a decimal.

**Solution:**

$\frac{3}{4}$ = $\frac{3\times25}{4\times25}$

= $\frac{75}{100}$

= 0.75.

= $\frac{75}{100}$

= 0.75.

**Question 3:**Convert $\frac{5}{4}$ to decimal.

**Solution:**

$\frac{5}{4}$

Divide 5 by 4, 5 ÷ 4

= 1.25

=> $\frac{5}{4}$ = 1.25.

Divide 5 by 4, 5 ÷ 4

= 1.25

=> $\frac{5}{4}$ = 1.25.