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 ?

**The answer is YES !!!**

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**.