Question

Is zero a rational number? Give reason for your answer.

Answer 1

Hint: First we are going to look at the definition of rational numbers and some of its properties and then we will see if zero satisfies all those properties or not.

Complete step-by-step solution -

So, let’s look at the definition of rational number,
A rational number is a number that can be in the form $\dfrac{p}{q}$ where p and q are integers and q is not equal to zero.
Zero satisfies the above definition.
Basically, the rational numbers are the integers which can be represented in the number line.
Closure Property: The closure property states that for any two rational numbers a and b, a + b is also a rational number.
So let b = 0 and ‘a’ is a rational number then we get a + 0 = a, hence zero satisfies this property.
Commutative property: For any two rational numbers a and b, a + b = b+ a.
Again let b = 0 and then we get a + 0 = 0 + a, which is true and hence zero satisfies this property.
Associative property: For any three rational numbers a, b, c we get $a+\left( b+c \right)=\left( a+b \right)+c$ .
Let b = 0 and then we get $a+(0+c)=(a+0)+c$ , hence both are equal so zero satisfies this property also.
And from this we can say that zero is a rational number.

Note: One should keep in mind the properties of rational numbers to solve this question and the definition of rational numbers is also important.