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: $$-\mathrm{\infty },\dots 0,1,2,3,4,5,\dots \mathrm{\infty }$$.
The number 5 is present in the integer numbers
Rational Numbers- Numbers that can be written in the form of $${\displaystyle \frac{p}{q}}$$ , where $$q\ne 0$$.
Example: $$0,3,5,-7,-100,{\displaystyle \frac{1}{2}},{\displaystyle \frac{5}{3}},0.16,0.4666\text{etc}\text{.}$$
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 $${\displaystyle \frac{p}{q}}$$
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: $$0,5,-7,\sqrt{2},{\displaystyle \frac{5}{3}}..\text{etc}\text{.}$$
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.