Question

Is 5 a rational, irrational, natural, whole, integer or real number?

Answer 1

Hint: In this question, we must state which number classification the number 5 belongs to. We need to talk about all of the different types of numbers that are contained in it, or a set of real numbers. In the section below, we'll look at some examples of distinct number classifications.

Complete step by step solution:
Natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers are all types of numbers in mathematics.
Natural numbers - All counting numbers that begin with 1 are included.
Example: All numbers such as 1, 2, 3, 4, 5, 6, …
The number 5 is present in the natural numbers.
Whole Numbers - A collection of natural and zero numbers.
Example: All numbers including 0 such as 0, 1, 2, 3, 4, 5, 6, …
The number 5 is present in the whole numbers
Integers- The collective result of whole numbers and negative of all natural numbers.
Example: \[-\infty ,\ldots 0,\,1,\,2,\,3,\,4,\,5,\ldots \infty \].
The number 5 is present in the integer numbers
Rational Numbers- Numbers that can be written in the form of \[\dfrac{p}{q}\] , where \[q\ne 0\].
Example: \[0,\,3,\,5,\,-7,\,-100,\,\dfrac{1}{2},\,\dfrac{5}{3},\,0.16,\,0.4666\,\,\text{etc}\text{.}\]
The number 5 is present in rational numbers.
Irrational Numbers- All the numbers which are not rational and cannot be written in the form of \[\dfrac{p}{q}\]
Example: \[\sqrt{2},\,\pi ,\,\sqrt{3},\,2\sqrt{2}\,\text{and}\,\sqrt{45}\,\text{etc}\text{.}\]
The number 5 is not an irrational number.
Real numbers: Real numbers can be defined as the union of both the rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”.
Example: \[0,\,5,\,-7,\,\sqrt{2},\,\dfrac{5}{3}..\,\text{etc}\text{.}\]
The number 5 is present in the real numbers.
Therefore, the number 5 is a rational, whole, integer and real number.

Note:
Some mathematical questions are thoroughly explained. The question here is regarding the number 0 and where it belongs in the number system. We should be aware of the various types of numbers categorised in mathematics and how they differ from one another. A better way to explain is to use an example.