Question

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

Answer 1

Hint: First, we will understand the definitions of given terms: - rational numbers, whole numbers, integers, and real numbers, by taking examples. Then we will try to eliminate the options – by – one to get the correct answer.

Complete step by step answer:
Let us consider the definitions of the terms given in the question one – by – one.
1. Natural numbers: - All counting are called natural numbers. For example - 1, 2, 3, 4, …… are examples of natural numbers.
2. Whole numbers: - The set of all-natural numbers together with 0 forms the set of whole numbers. For example: - 0, 1, 2, 3, 4,…. Are the examples of whole numbers.
2. Integers: - Integers are defined as the set of whole numbers together with the set of negative of natural numbers. For example: - ….., -3, -2, -1, 0, 1, 2, 3, ….. are included in the set of integers.
4. Rational numbers: - A rational number is a number that can be written in the form $${\displaystyle \frac{p}{q}}$$ where p and q are integers and $$q\ne 0$$. Since q can be equal to 1 so we can say that every natural number, whole number, and integer are included in the set of rational numbers.
5. Real numbers: - Real numbers are defined as the set of all rational and irrational numbers.
On reading the above definitions we can eliminate some of the options by taking an example like $${\displaystyle \frac{4}{3}}$$. Here, we can see that both 4 and 3 are integers so it is rational in nature.
From the above definitions, we can say that$${\displaystyle \frac{4}{3}}$$ is not a natural number, whole number or integer because it is a fraction. So, these options are eliminated. Now, from the definition of real numbers, we can clearly conclude that $${\displaystyle \frac{4}{3}}$$ is a real number. Therefore, every rational number is a real number.
Hence, the option (c) is the correct answer.

Note:
One may note that we must know the definitions of basic terms used in the questions otherwise it will be difficult to determine the correct option. Remember that every rational rational number is a real number but every real number is not a rational number because there is another set called irrational numbers which cannot be represented in the form $${\displaystyle \frac{p}{q}}$$. You may remember that in short: - Natural numbers $$\subset$$ whole numbers $$\subset$$ Integers $$\subset$$ Rational numbers $$\subset$$ Real numbers. Here, $$\subset$$ is the symbol to denote a subset.