Question

Is $\dfrac{1}{4}$ a rational, irrational, natural, whole, integer or real number ?

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. So, let us see how to solve this problem.

Complete step by step answer:
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 $\dfrac{1}{4}$ satisfies which of the definitions.

Real Numbers: Real numbers are simply the combination of rational and irrational numbers, in the number system. For example, $23, - 12,6.99,\dfrac{5}{2}....$ So, $\dfrac{1}{4}$ is rational as it is in the form $\dfrac{p}{q}$ and $q$ is not equal to zero.

Therefore, $\dfrac{1}{4}$ is also a real number, but to be more specific and precise it is a rational number.

Note: Every rational number is a real number, but not every real number is a rational number. The set of real numbers is the superset of the set of rational numbers. Integers and whole numbers sets are also the subsets of real number sets. But the complex number set is not a subset of the real number set.