# Chapter 2 – Whole Numbers

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

There are many numbers in the world that can be divided into whole numbers, natural numbers, integers, etc. Can one really count all the numbers? It would be like counting stars in the sky. However, numbers play a very integral role in our daily lives and complex scientific problems.

Let us begin with a basic understanding of the number system. A numeral system or the number system is a system of expressing numerical digits or numbers in an organized and classified format.

Every number known to humankind is classified into various sets for a better understanding and better usage. These sets may be called natural numbers, rational numbers, irrational numbers, integers, whole numbers, etc.

In this article, we will be learning about whole numbers.

#### Definition

Whole numbers are numbers that begin from 0 and go on till infinity.

These numbers are denoted by the letter W.

Whenever you are asked to count numbers, you start counting 1, 2, 3, 4, and so on…

This counting method is a natural occurrence, and therefore natural numbers begin from 1 and go till infinity.

However, in 628 BC, the famous Indian Mathematician Brahmagupta introduced the number 0, and it became the foundation for designing the system of whole numbers.

Interesting Fact: Every natural number is a whole number but not every whole number is a natural number.

#### Properties of Whole Numbers

• Closure property

The closure property of whole numbers states that the multiplication or addition of any two whole numbers will result in a whole number as well.

For example: Let us take two whole numbers, 2 and 3

2X3= 6 (which is also a whole number)

2+3=5 (which is also a whole number)

• Commutative property

The commutative property of whole numbers states that the addition or multiplication of two whole numbers will also result in a whole number regardless of their order of addition or multiplication.

For example: Let us take two whole numbers 2 and 3

2×3 = 3×2

2+5 = 5+2

• Additive identity property

The additive identity property of the whole numbers states that its value remains unchanged when a whole number is added to zero.

For example: Let us take a whole number 5

5+0 = 5

• Multiplicative property

The multiplicative property of whole numbers states that its value remains unchanged when a whole number is multiplied with 1.

For example: Let us take a whole number 5

5×1= 5

• Associative property

The associative property of whole numbers states that the manner of the grouping of the numbers does not affect the result in the case of multiplication or addition.

For example: Let us take three whole numbers 2,3, and 4.

(2×3)x4 = 2x(3×4)

(2+3)+4 = 2+(3+4)

• Distributive property

The distributive property of whole numbers states that when multiplication and addition/subtraction are seen together, the effect of the number outside the bracket falls upon every number inside the bracket.

For example: Let us take three whole numbers, 5,6, and 7.

7x(6+5) = (7×6) + (7×5)

7x(6-5) = (7×6) – (7×5)

#### Patterns of Whole Numbers

The entire set of whole numbers can be divided into various patterns, namely

• Ascending
• Descending
• Odd numbers
• Even numbers
• Multiples of a number
• Square numbers
• Cube numbers etc.

#### FAQs

1. What are whole numbers for Class 6?

In mathematics, whole numbers are a part of Real Numbers.

These numbers begin from 0 and go on up to infinity.

On the number line, they begin from the number 0 and move forward on the right side.

The set of whole numbers is an uncountable set.

2. What is meant by whole numbers for Class 6?

The basic counting numbers that begin from zero and go on up to infinity are known as whole numbers. These numbers are used in daily life, from nutrition labels to the numbers on a TV remote.

Whole numbers are denoted by the letter W and are a subset of Real numbers.

3. Which is the smallest whole number for Class 6?

Since the whole numbers begin from the number 0 on the number line, any number before the number 0 will not be a part of the set of whole numbers. This means that the number 0 is the smallest whole number, and the largest whole number is infinity.

The whole numbers set is 0, 1, 2, 3…infinity.

4. How many whole numbers are there?

There are infinite whole numbers. Counting all the whole numbers would be like counting the stars in the sky.

The set of whole numbers is an uncountable one. This means that there is no definite answer to how many whole numbers are there since the numbers go up to infinity.

5. Which is the smallest number?

While 0 is the smallest whole number and 1 is the smallest natural number, one can never say the smallest number on the number line.

This is because the number line’s assumed midpoint is zero, and the numbers (both negative and positive) go up to infinity.

Therefore, the smallest number on the number line would be an infinite number.

6. Which is the smallest whole number?

Whole numbers (denoted by the letter w) are a subset of Real Numbers and a superset of Natural numbers.

Whole numbers begin from the number 0 and go on up to infinity.

Thus making 0 the smallest whole number.

The numbers that begin from zero and move forward on the right side of zero on the number line are called whole numbers. These whole numbers are a subset of real numbers and are denoted by the letter W. Various properties apply to them (as mentioned above).

We understand that the study of numbers can be overwhelming and a little complex at times. For a better understanding of the whole numbers, try MSVgo, the Math Science Super App that facilitates informative videos on various topics of science and math that help you understand better and grow faster.

### High School Physics

• Alternating Current
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• Wave Optics
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### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
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### High School Biology

• Absorption and Movement of Water in Plants
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• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
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• Binomial Theorem
• Calculus – Applications of Derivatives
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• Permutations and Combinations
• Probability
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• Trignometry – Height and Distance
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### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Chemistry in Your Life
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• Transportation In Animals And Plants
• Universe
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• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Addition
• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time
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