[Maths Class Notes] on Whole Numbers Pdf for Exam

A number system is a writing system that frequently uses numbers or other symbols to describe a certain set. It provides a unique representation of each number and the arithmetic and algebraic structure of the figures. It also allows us to perform arithmetic operations like addition, subtraction, and division. Let us now know in this article about the meaning and properties of whole numbers, which are a part of the number system.

Whole Numbers Definition

The whole numbers are numbers without fractions. They are a set of positive integers and zero. Whole numbers are shown as ‘W’ and the number set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…………}.

Including zero, all figures are true and do not include either fractional or decimal sections i.e. 3/4, 2.2, or 5.5 are not entire quantities. So, these are not whole numbers. Furthermore, with all the numbers, subtraction, multiplication, and division operations are necessary.

If you are in trouble again, what is the actual amount in mathematics? The accompanying explanation offers a more comprehensive understanding of the whole count.

An integer that is 0 and greater than 0 is a whole sum. The first five numbers in all were 0, 1, 2, 3, and 4. They all go up to infinity.

The whole numbers are almost the same as natural numbers except for 0. Since integers range from negative infinity to positive infinity, total whole numbers are a subset of integer numbers.

The whole number set is expressed by using the basic mathematical definition of a set W = {0, 1, 2, 3,…..} as a collection of objects that share a well-defined property. Beginning with 0, the element x of the set is created by adding the number before x to its predecessor, which is x-1. Using an ellipsis (…) implies the number of elements in the set is not finite (i.e., infinite).

With the exception of 0, every number x has precisely one immediate predecessor — the amount that falls before x. Each number y has exactly one immediate counterpart — the number after y.

An interesting feature of the whole set of numbers is that there is no largest whole number. Suppose b is the highest whole number, so b + 1 is a whole number. Nevertheless, b + 1 is greater than b. This approach reveals that you can always find a bigger whole number.

Whole Numbers Properties

Complete number properties are based on mathematical operations such as combining, subtracting, splitting, and multiplying. If inserted, subtracted or combined; two whole numbers may form the entire number itself. As a result, we can also get a fraction in the division method. Here are different properties of whole numbers.

Closure Property

Combining the two whole numbers forms a whole number. i.e. if x and y are two entire numbers then x × y or x + y is an entire number, too.

Commutative Property of Addition and Multiplication

The sum and product of any of the two whole numbers are the same regardless of the order in which they are added or multiplied, i.e. if x and y are two full numbers x + y = y + x and x × y = y × x.

Additive Identity

If a whole number is added to 0, its value remains unchanged, i.e. when x is a whole number then the equation can be written as: 

x + 0 = 0 + x.

Associative Property

When adding or multiplying whole numbers as a set, they can be grouped in any order, and the result will be the same, i.e. if x, y, and z are full numbers then the equation can be expressed as

x + (y + z) = (x + y) + z


x · (y · z) = (x · y) · z

Distributive Property

When x, y, and z are three complete digits, the multiplication over distributive property is given by:

x × (y + z) = (x × y) + (x × z)

Likewise, the multiplication over subtraction distribution property is given by:

x × (y – z) = (x × y) – (x × z)

Can Whole Numbers 

The whole number cannot be negative! The reason for the same has been stated below:

  • As per the definition of whole numbers, the number line as stated {0, 1, 2, 3, 4, 5, 6… till positive infinity} are constituted in the whole numbers line.

  • There is no place for negative numbers in the whole numbers line.

Is 0 a Whole Number?

The set of numbers contains all the natural numbers, along with zero. So yes, 0 (zero) is not only a whole number but it is also the first whole number.

Multiplication by Zero

By multiplying a whole number with 0, the answer will always be 0, i.e. X × 0 = 0 × X = 0.

Division by Zero

The whole number division by 0 is not specified, i.e. when x is a whole number, x/0 is not defined.

Some Facts About the Whole Numbers

  1. There is no single number that can be called ‘big’.

  2. Besides 0, all values have an immediate predecessor or a number that falls before them.

  3. There is a decimal number or a percentage for two whole quantities, but not whole numbers.

Difference Between Whole Numbers and Natural Numbers

Whole Numbers

Natural Numbers

Whole numbers are:

(0, 1, 2, 3, 4, 5, 6…)

Natural Numbers are:

(1, 2, 3, 4, 5, 6…)

The counting of whole numbers starts from the number ‘0’.

The counting of natural numbers starts with the number ‘1’.

All the numbers on the whole numbers line are not natural numbers.

All the numbers on the natural numbers line are whole numbers.

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