# 0 is a rational number ?

In this chapter, we will try to answer the question “ if 0 is a rational number ? “.

To understand the concept you should have good understanding of the concept of rational number.

Let us revise the concept of rational number then will move on to answer above question.

## Rational number and its representation

The numbers which can be expressed in the form of P / Q are called rational numbers.

Where P & Q are integers which can be positive or negative.

Number like \mathtt{\frac{33}{7} ,\ \frac{21}{4} ,\ 13.25,\ 11.751} are examples of rational numbers.

### But why decimals like 13.25 & 11.751 are part of rational numbers?

Because these decimals can be easily converted in the form of P / Q.

\mathtt{13.25\ \Longrightarrow \ \frac{1325}{100}}\\\ \\ \mathtt{11.751\ \Longrightarrow \ \frac{11751}{1000}}

### Are there any decimals which doesn’t belongs to rational number group ?

Yes, decimal numbers which cannot be converted back into fraction are not part of rational numbers.

Examples;

(i) 𝜋 = 3.14159 . . .

The value of pi cannot be converted into fraction. Hence, it is irrational number.

(ii) \sqrt{2} = 1.414 . . .

The value of \sqrt{2} cannot be converted into fraction. Hence, it is irrational number.

## Is 0 a rational number ?

Because 0 can be represented in the form of P / Q.

If we insert any denominator on number 0, the number will still remain 0.

For example;
Inserting denominator 5.

0 can also be written as \mathtt{\ \frac{0}{5}}

i.e. \mathtt{0\ \Longrightarrow \ \frac{0}{5}}

You can see that we can easily represent 0 in the form of P / Q.

Hence, 0 is a rational number.