Question

Is the number $\dfrac{2}{3}$ a rational, irrational, natural, whole and integer?

Answer 1

Hint: By using examples, we will first grasp the definitions of the following terms: rational numbers, irrational numbers, whole numbers, integers, and natural numbers. Then, one by one, we'll strive to remove the possibilities until we find the proper answer.

Complete step-by-step solution:
We will understand the definition of each term one by one:
Natural numbers: All numbers that can be counted are referred to as natural numbers. Natural numbers include, for example, 1, 2, 3, 4, and so on.
Whole number: The set of whole numbers is formed by the set of all-natural numbers plus 0. For example: - 0, 1, 2, 3, 4,....
Integer number: The set of whole numbers plus the set of negative natural numbers is known as an integer. The set of numbers includes, for example-…, -3, -2, -1, 0, 1, 2, 3,.....
Rational number: A rational number is one that can be represented in the form $\dfrac{p}{q}$ , where p and q are integers and q is not equal to zero. We can claim that every natural number, whole number, and integer is included in the set of rational numbers because q can be equal to 1.
Irrational number: Irrational numbers are defined as the real numbers which cannot be written in the simple fraction form of $\dfrac{p}{q}$, where ‘p’ and ‘q’ are integers and q is not equal to zero.
We can now check $\dfrac{2}{3}$ satisfies which of the definitions.
So, $\dfrac{2}{3}$ is rational as it is in the form $\dfrac{p}{q}$ and q is not equal to zero.

Note: It's worth noting that we need to know the definitions of basic phrases used in the questions; otherwise, determining the correct selection will be tough. Remember that every rational number is a real number, but not every real number is a rational number.