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.