**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

**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 come**s naturally to a kid**.

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 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

**(c) Commutative Property of Whole number**

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

**(d) Distributive Property of Whole number**

**Frequently Asked Question – Whole Number**

**Are all natural numbers also part of whole numbers?**

YES!!

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?**

NO!!

Whole number 0 is not part of the natural number

**Can whole number be negative?**

NO!!

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

**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.