Question

Every whole number is
A.an integer
B.irrational
C.fraction
D.none of these

Answer 1

Hint: First we will recollect the definition of a whole number. Then, we will recollect the definition of the terms given in the options. Then, we will see which option is satisfying the condition of whole numbers and we will choose that option.

Complete step-by-step answer:
First, we will state the definition of whole numbers:-
Whole numbers are those numbers that can be expressed without the help of any fraction or decimal. They are non-negative. They include 0 and positive numbers. Examples of whole numbers are 0, 1, 2, 3, etc.
Now let us have a look at option A.
An integer is any number that can be represented as a whole; that is integers are those numbers that can be expressed without a fractional component or a decimal component. Integers can be positive, negative or 0. Some examples of integers are $$-1$$ , $$-2$$, $$-3$$, $$0$$, $$1$$, $$2$$, etc.
We can make out from the definition that all non-negative integers are whole numbers. So it is correct to say that all whole numbers are integers.
Option A is correct.
Let us look at option B, irrational numbers. Irrational numbers are numbers that can’t be expressed in the form $${\displaystyle \frac{p}{q}}$$ where $$p$$ and $$q$$ are integers. Every whole number can’t be an irrational number because every whole number $$w$$ can be expressed in the form $${\displaystyle \frac{p}{q}}$$ as $${\displaystyle \frac{w}{1}}$$. So option B is incorrect.
Let us look at option C, fraction. Every whole number cannot be a fraction because fractions are used to represent the numbers that are not whole. Fractions are numbers that can be represented as decimals but not as whole numbers. For example, $${\displaystyle \frac{1}{2}}$$ is a fraction that is equal to $$0.5$$and is not a whole number.
From the above discussion, we can conclude that the correct option is A, an integer.

Note: We know that different numbers can be represented in the form sets in the following manner:
$$\mathrm{N}\subseteq {\mathrm{N}}_0\subseteq \mathrm{Z}\subseteq \mathrm{Q}\subseteq \mathrm{R}$$ .
Here, $$\mathrm{N}$$ are natural numbers, $${\mathrm{N}}_0$$ are whole numbers, $$\mathrm{Z}$$ are integers, $$\mathrm{Q}$$ are rational numbers and $$\mathrm{R}$$are real numbers.
 We can directly look at this relationship and conclude that whole numbers are a subset of integers. This means that all whole numbers are included in the set of integers.