Question

Every rational number is
(a) A natural number
(b) An integer
(c) A real number
(d) A whole number

Answer 1

Hint: Use the definition of each of the different forms of numbers to check each of the given options. Give an example or a counterexample to check if each of the options is correct or not.

Complete step-by-step answer:
We have to check in what all forms can we write any rational number as.

We know that a rational number is a number that can be expressed in the form $\dfrac{p}{q}$, where ‘p’ and ‘q’ are integers and $q\ne 0$.

We will now check if we can write any rational number as other forms of numbers given in the options.

We will firstly consider natural numbers. We know that natural numbers are positive integers $1,2,3,..$ .

Let’s assume that our rational number is $\dfrac{2}{3}$. We observe that $\dfrac{2}{3}$ is not a natural number.

Thus, all rational numbers can’t be natural numbers.

Hence, option (a) is incorrect.

We will now consider integers. Integers include all positive and negative numbers that don’t

have a fractional part. Integers include numbers of the form $...-3,-2,-1,0,1,2,3,...$.

Let’s assume that our rational number is $\dfrac{2}{3}$. We observe that $\dfrac{2}{3}$ is

not an integer.

Thus, all rational numbers can’t be integers.

Hence, option (b) is incorrect.

We will now consider real numbers. Real numbers are numbers comprising all rational and irrational numbers. It includes all those numbers which can be represented on a real line.
Thus, all rational numbers are real numbers.

Hence, option (c) is correct.

We will now consider the whole numbers. We know that whole numbers are all non - negative integers $0,1,2,3,..$ .

Let’s assume that our rational number is $\dfrac{2}{3}$. We observe that $\dfrac{2}{3}$ is not a whole number.

Thus, all rational numbers can’t be whole numbers.

Hence, option (d) is incorrect.

Hence, all rational numbers can be real numbers, which is option (c).

Note: One must know the definition of all forms of numbers to solve this question. One must observe that natural numbers are a subset of whole numbers, whole numbers are a subset of integers, integers are a subset of rational numbers and rational numbers are a subset of real numbers.