If you are going to read what is called a Whole Number on this page, then definitely read the article completely.
On the previous page, we have shared information about Odd Numbers, so do read odd numbers.
Let us read and understand the properties and rules of what is called a whole number on this page.
Whole Numbers Definition
All positive natural numbers from 0 to infinity are called whole numbers.
The Whole Numbers are the numbers without fractions and it is a collection of positive integers and zero.
It is represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}. Zero as a whole represents nothing or a null value.
Whole Numbers : W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10……}
Natural Numbers : N = {1, 2, 3, 4, 5, 6, 7, 8, 9,…}
Integers : Z = {….-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…}
Counting Numbers : {1, 2, 3, 4, 5, 6, 7,….}
These numbers are positive integers including zero and do not include fractional or decimal parts (3/4, 2.2 and 5.3 are not whole numbers).
Also, arithmetic operations such as addition, subtraction, multiplication and division are possible on whole numbers.
Symbol
The symbol to represent whole numbers is the alphabet ‘W’ in capital letters.
W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…}
Thus, the whole numbers list includes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ….
Whole Numbers on Number Line
Rules of Whole Numbers
There are 6 properties of whole numbers.
- Closure properties of whole numbers
- Commutative rule of addition
- Commutative rule of multiplication
- Associative law of sum
- Associative rule of multiplication
- For whole numbers, multiplication over addition is distributive.
1). Closure Properties of Whole Numbers
Whole numbers are closed under addition and multiplication. Adding or multiplying any two whole numbers gives a whole number.
Example :-
7 + 2 = 9, 7 x 9 = 63
Hence 9, 63 is a whole number.
2). Commutative Rule of Addition
Whole numbers follow the commutative rule in addition. Adding any 2 or more than 2 whole numbers in any order gives the same answer.
Example :-
- 1 + 2 + 3 + 4 + 5 = 15
- 5 + 2 + 4 + 1 + 3 = 15
3). Commutative Rule of Multiplication
Whole numbers follow the commutative rule in multiplication. Multiplying any 2 or more than 2 whole numbers in any order gives the same answer.
Example :-
- 9 × 6 = 54
- 6 × 9 = 54
4). Associative Law of Sum
All whole numbers follow the associativity rule in addition.
5). Associative Rule of Multiplication
All whole numbers obey the multiplication associative rule.
6). For Whole Numbers, Multiplication over Addition is Distributive.
Difference Between Whole Numbers and Natural Numbers
Let us understand the difference between natural numbers and whole numbers with the help of the table given below :
| Whole Numbers | Integer Number |
|---|---|
| All positive natural numbers from 0 to infinity are called whole numbers. For example :- 1, 2, 3, 4, 5, 6, 7, 8, 9 …………….infinite | The numbers made up of positive, negative and zero are integer numbers. Ex : -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 |
| The set of whole numbers is represented by ‘W’ (Whole Number). Whole numbers (W) = 1, 2, 3, 4, 5, 6, 7, 8, 9………..infinite | The set of whole numbers is represented by ‘I’ (Integer Number). Integer numbers (I) = -4, -3, -2, -1, 0, 1, 2, 3, 4, |
| All natural numbers are whole numbers. But all whole numbers are not natural numbers. | All whole numbers and their negative numbers are called integers. |
Facts :
- All the natural numbers are whole numbers
- All counting numbers are whole numbers
- All positive integers including zero are whole numbers
- All whole numbers are real numbers
Examples of Whole Numbers
Q.1 What is the smallest whole number?
A.0
B.1
C.2
D.4
Ans. 0 is the smallest whole number.
Q.2 What is the largest whole number?
A.0
B.1
C.2
D. cannot be defined
Ans. The largest whole number cannot be defined.
Q.3 The number starting from zero and going to infinity is called?
A. natural numbers
B. whole numbers
C. integer numbers
D. even numbers
Ans. whole numbers
Q.4 What are the natural numbers including zero called?
A. natural numbers
B. whole numbers
C. integer numbers
D. prime numbers
Ans. whole numbers
Q.5 What is a one digit number?
A.8
B.9
C.7
D.10
Ans. 10
Hope you have liked the information about whole numbers.
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