Question

Is 0 a rational, irrational, natural, whole, integer or real number?

Answer 1

Hint: Here in this question, we have to say to which classification of numbers the number 0 belongs to. We have to discuss the topic of all the different types of numbers included in it or a set of real numbers and Examples of different classification of numbers are explained in the below section.

Complete step-by-step answer:
In mathematics we have different kinds of numbers namely, natural number, whole number, integers, rational numbers, irrational numbers and real numbers.
Natural numbers - Contain all counting numbers which start from 1.
Example: All numbers such as 1, 2, 3, 4, 5, 6,…
The number 0 is not present in the natural numbers.
Whole Numbers - Collection of zero and natural numbers.
Example: All numbers including 0 such as 0, 1, 2, 3, 4, 5, 6,…
The number 0 is present in the whole numbers
Integers- The collective result of whole numbers and negative of all natural numbers.
Example: \[ - \infty , \cdot \cdot \cdot 0,1,2,3, \cdot \cdot \cdot + \infty \]
The number 0 is present in the integers.
Rational Numbers- Numbers that can be written in the form of \[\dfrac{p}{q}\] where \[q \ne 0\]
Example: 3, -7, -100, \[\dfrac{1}{2}\], \[\dfrac{5}{3}\], 0.16, 0.4666 etc
The number 0 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: \[\sqrt 2 \], \[\pi \], \[\sqrt 3 \], \[2\sqrt 2 \] and \[ - \sqrt {45} \] etc
The number 0 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, -7, \[\sqrt 2 \], \[\dfrac{5}{3}\]..etc.,
The number 0 is present in the real numbers.
Therefore the number 0 is a rational, whole, integer and real number.

Note: Some questions in mathematics are explained in a detailed way. Here the question is about the number 0 and in which classification of numbers it is present. We should know about the different kinds of numbers that are classified in mathematics and how they are different from each other. Better to explain with an example.