Question

Is $3$ a rational number?

Answer 1

Hint: Here we have to check if the above given number is a rational number. So we will first try to understand the definition of a rational number and its property. Then we will try to express the given number i.e. $3$ in the form of a rational number. If it can be expressed then the given number is a rational number and if not the given number is not a rational number.

Complete step-by-step answer:
Let us understand the definition of a rational number:
A rational number can be defined any number which can be represented in the form of
 $\dfrac{p}{q}$ , where $p$ and $q$ are integers and $q \ne 0$.
The set of rational numbers includes positive numbers, negative numbers and zero.
We should know that every whole number on the number line is a rational number because every whole number can be expressed in the form of $\dfrac{p}{q}$ .
Now in the question we have been given a number $3$ .
We know that the given number is a whole number. Let us try to represent the number in the fraction form.
We can write $3$ in the fraction form i.e.
 $\dfrac{3}{1} = \dfrac{p}{q}$ .
Here we have
$p = 3,q = 1$ and the denominator is not equal to zero i.e. $q \ne 0$ .
This proves that the given number is a rational number.
Hence we can say that $3$ is a rational number.

Note: We should note that the above number can also be expressed in the other forms of fractions i.e. $\dfrac{6}{2} = 3$
And,
$\dfrac{{12}}{4} = 3$ .
These all fractions are given the same value.
We should know some of the properties of a rational number like that if we add , subtract or multiply two rational numbers, they always give another rational number.
For example, let us take two rational numbers : $5$ and $10$ .
Now we will add them to see the result:
$5 + 10 = 15$