Whole Numbers

Whole number is a natural number that is not a fraction or a decimal. Whole numbers are positive, negative, or zero. Numbers are symbols that represent quantities. They can be used to represent anything from the number of days in a month to the number of planets in the solar system.

Whole Numbers Definition and Examples

A whole number is a natural number that is not a fraction or a decimal. Whole numbers are positive, negative, or zero. Whole numbers is represented by “W” and the set of the numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………. 0 as a whole represents null value or nothing.

These given numbers above are positive integers together with zero and additionally do no longer consist of decimal or fractional parts (3/4, 2.2 and 5.3 are not an whole numbers). Arithmetic operations such as subtraction, addition, division and multiplication are possible on whole numbers.

Whole Numbers Symbol

The Whole Numbers is represented through the symbol ‘W’ in capital letters. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…}. Therefore, the whole numbers list consist of (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ….).

Whole Numbers Properties

A whole number is a number that can be divided evenly by two without a remainder. Whole numbers are also positive integers. The set of whole numbers includes the number zero, 1, 2, 3, 4, 5, 6, 7, 8, 9, and all positive integers that follow.

Some properties of whole numbers include:

• Whole numbers are positive integers.
• Whole numbers can be divided evenly by two without a remainder.
• The set of whole numbers includes the number zero, 1, 2, 3, 4, 5, 6, 7, 8, 9, and all positive integers that follow.

Closure Property

They can be closed under both the multiplication and addition, i.e., if a and b are the two whole numbers then a. b or a + b is also a whole number.

Example:

6 and 7 are whole numbers.

6 + 7 = 13; a whole number

6 × 7 = 42; a whole number

Commutative Property of Addition and Multiplication

For all real numbers a and b,

a + b = b + a

a · b = b · a

Example: Consider two whole numbers 6 and 7.

Solutions: 6 + 7 = 13

7 + 6 = 13

Thus, 6 + 7 = 7 + 6 .

Also,

6 × 7 = 42

7 × 6 = 42

Therefore, 3 × 7 = 7 × 3

Additive Identity

The additive identity is zero. This means that when you add zero to any number, the result is the original number. For example, if you add zero to 5, you get 5. If you add zero to -5, you get -5.

Example: Let us consider two whole numbers 0 and 5.

Solutions: 0 + 5 = 5

5 + 0 =5

Thus, 0 +5 = 5 + 0 = 5

Associative Property

The associative property states that when you group things together, the order of the grouping doesn’t matter. So, for example, 2+3+4=7, 7+4=11, and 11+2=13.

Distributive Property

The distributive property states that for every number a, there is a number b so that a + b = ab.

List of Whole Numbers from 1 to 100

All numbers from zero to infinity are the whole numbers, while counting the whole numbers between 1 and 100, no numbers are left and all numbers are considered as a whole numbers. There are 100 whole numbers from 1 to 100. In this given list the smallest whole number is 1 and the largest whole number is 100. Therefore the list containing all the numbers from 1 to 100 is-

Whole Numbers from 1 to 100

Can Whole Numbers be Rational Numbers?

No, whole numbers cannot be rational numbers. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Whole numbers are numbers that can be expressed as a whole number, without any fractions.

Is 0 a Whole Number?

Yes, 0 is considered a whole number. Whole numbers include all the non-negative integers, including zero. They are the numbers 0, 1, 2, 3, and so on, with no fractions or decimals.

Multiplication by Zero

When the any whole number is multiplied to 0, the result is always 0, i.e., a x 0 = 0 x a = 0

Example:

0 × 7 = 0

7 × 0 = 0

Here, 0 × 7 = 7 × 0 = 0

Division by Zero

The division of any whole number by o is not defined, i.e., if p is a whole number then p/0 is not defined.

Also Check:

Difference Between Natural Numbers and Whole Numbers

• The difference between whole numbers and natural numbers is that whole numbers are the counting numbers that include the number zero, while natural numbers are the counting numbers that exclude the number zero.
• A whole number is any integer (positive or negative) that can be expressed without a fractional component. A natural number is simply a whole number that is not zero. The difference between whole numbers and natural numbers is that whole numbers can be negative (e.g. -5), while natural numbers cannot be negative.

Some Facts About the Whole Numbers

• The whole numbers are the natural numbers and the integers.
• The whole numbers are the set of numbers that includes the natural numbers and the integers.
• The whole numbers are the set of numbers that includes the counting numbers.
• The whole numbers are the set of numbers that includes the counting numbers and the integers.
• The whole numbers are the set of numbers that includes the counting numbers, the integers, and the rational numbers.
• The whole numbers are the set of numbers that includes the counting numbers, the integers, and the irrational numbers.

Frequently Asked Questions on Whole Numbers

what is a whole number in math?

A whole number is a non-negative integer without fractional or decimal parts.

Why is 0 a whole number?

Zero is a whole number because it represents the absence of quantity.

Is 1 to 100 are all whole numbers?

Yes, 1 to 100 are all whole numbers.

What are whole numbers used for?

Whole numbers are used in counting, calculations, and representing discrete quantities.

Is 0 the first number or 1?

In mathematics, 0 is neither the first nor second number. It is the starting point for counting, but 1 is typically considered the first number in a sequence.