What are Whole Numbers?

Whole Number Definition

All positive integer number from 0 to infinity are known as whole numbers

Whole numbers so not include fractions or decimals

Key Features of Whole Number
(a) Positive integers
(b) 0 is part of whole number
(c) Does not include decimals or fraction

Set Representation of whole numbers

In mathematics, whole numbers can be represented in form of sets.

Below are some examples:

(a) W = Set of positive integers starting from 0

(b) W = { 0, 1, 2, ,3, 4, 5, 6 . . .}

(c) W = {x : x is an integer starting from 0}

Here, W is symbol representing whole number

Example of Whole Numbers

Some numerical examples are:
0, 20, 90, 60, 149, 192, 1001, 9999…….

Numbers which are not whole numbers
-32, 1.54, -93, 2.8, 9.1

Whole numbers on Number line

Below image represent the whole number in number line format.

Note that the number line start from 0 and then move towards infinity

Representing whole numbers on number line

Whole Numbers and Natural Numbers

Understanding natural number is very easy. Just ask a kid to start counting numbers and the kid will go like: 1, 2, 3, 4, 5, 6 . . . . .

Hence the number starting with 1 and that goes to infinity are natural numbers.
In fact, the natural number can be understood as number which comes naturally to a kid.

Whole numbers and natural numbers

So technically we can write natural numbers as:

N= {1, 2, 3, 4 . . . . . . .}

Now let us understand the whole numbers.
Whole numbers are natural numbers with 0.

Hence, if we add 0 in the set of natural numbers it gets complete and whole in itself.
Technically we can represent whole numbers as:

W= {0, 1, 2, 3, 4 ……..}

Are all whole numbers part of integers?

All the non-decimal positive and negative numbers including 0 are integers.

And we know that whole numbers are positive integers.

So yes, all whole numbers are integers.

Now questions arises if all integers are whole numbers?

The answer is NO.

Integers include negative numbers which doesn’t come under whole number

Whole numbers and integers

Whole numbers and Rational numbers

Rational numbers are the ones which can be represented in the form of p/q

\mathtt{\frac{3}{5} ,\ \frac{7}{13} \ and\ \frac{-\ 9}{14}}

All the whole numbers are form of rational numbers as they can expressed in form of p/q

\mathtt{\frac{8}{1} ,\ \frac{0}{1} \ and\ \frac{\ 99}{1}}

Whole number properties

Given below are some of the properties of whole numbers:

(a) Closure property

It says that addition and multiplication of whole number will result in a whole number

A + B = C

A x B = C

If A & B are whole number then number C is also whole number

(b) Associative Property

The addition and multiplication of whole number will give same result even after regrouping of numbers

Properties of whole numbers

(c) Commutative Property of Whole number

The addition and multiplication of whole number will given same results even after interchanging digits

Whole numbers definition

(d) Distributive Property of Whole number

example of whole numbers

Frequently Asked Question – Whole Number

Are all natural numbers also part of whole numbers?

Natural Numbers are part of whole numbers.
As said earlier, natural numbers are represented as {1, 2, 3, 4 ……}; these numbers are all part of whole numbers.

Are all whole numbers also natural numbers?

Whole number 0 is not part of the natural number

Can whole number be negative?

Whole numbers are only positive numbers.
So numbers like -10, -1, -23 are not part of whole numbers

What is the smallest whole number?

Zero is the smallest whole number

Some practical application of whole numbers

1. Helps in counting votes
Imagine two candidates stand for presidential election.
After voting, counting is done to find the winner. For counting we need the help of whole numbers

Application of whole numbers

2. Attendance in School
Everyday teachers take attendance of the students sitting in the class.
After attendance, counting is done to find the number of student absent in particular day. This counting is done with the help of whole numbers.

Learn about whole numbers for grade 6 Math

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