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Whole Numbers: Meaning, Properties, and Examples

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What is the Difference Between Whole Numbers and Natural Numbers?

The concept of whole numbers is a basic building block in mathematics and is essential for understanding number systems, arithmetic calculations, and many daily situations. Knowing what whole numbers are helps students avoid common exam mistakes and quickly solve numerical problems. Let’s explore what whole numbers mean, their properties, and how you can recognize them easily.


What Is Whole Numbers?

A whole number is any of the numbers in the set {0, 1, 2, 3, ...}. These numbers do not have fractions, decimals, or negative signs. Whole numbers start from zero and go up to infinity. You’ll find this concept used in number system basics, counting, measurements, and coding in computer science.


Key Features of Whole Numbers

Property Explanation
Non-negative Whole numbers are never negative; they start from 0 upwards.
No fractions or decimals Numbers like 2.5 or 3/4 do not count as whole numbers.
Symbol Represented by W; for example, W = {0, 1, 2, ...}

Whole Numbers vs Natural Numbers

Whole Numbers Natural Numbers
0, 1, 2, 3, ... 1, 2, 3, 4, ...
Begins with zero Begins with one
Wider set (includes 0) Subset of whole numbers (does not include 0)

For more, see: Natural Numbers


Properties of Whole Numbers

  • The sum (addition) of any two whole numbers is always a whole number. (Closure property)
  • The product (multiplication) of any two whole numbers is also a whole number. (Closure property)
  • Order doesn’t matter for addition or multiplication: a + b = b + a; a × b = b × a (Commutative property)
  • Grouping doesn’t affect the result: (a + b) + c = a + (b + c) (Associative property)
  • Multiplication distributes over addition: a × (b + c) = a×b + a×c (Distributive property)
  • Zero is the additive identity: a + 0 = a
  • One is the multiplicative identity: a × 1 = a

For an in-depth study, visit Properties of Whole Numbers.


Examples of Whole Numbers

Number Whole Number? Reason
0 Yes Whole numbers start at 0
15 Yes It is in the set {0,1,2,...}
−2 No Negative, so not whole number
8.5 No Decimal, not allowed
100 Yes Belongs to whole numbers

Whole Numbers on the Number Line

Whole numbers can be shown on a number line by marking points starting from 0 and moving to the right: 0, 1, 2, 3, 4, ... Each number is spaced equally. This visual is helpful for understanding addition, subtraction, and how numbers increase.

To learn more or practice number line problems, see Whole Numbers on Number Line.


Try These Yourself

  • List the first five whole numbers.
  • Is 0 included in whole numbers? Why?
  • Find all whole numbers between 10 and 16.
  • Select the ones that are not whole numbers: 7, −3, 5.2, 20.

Frequent Errors and Misunderstandings

  • Confusing whole numbers with natural numbers—remember, whole numbers include 0.
  • Thinking negative numbers are whole numbers—they are not.
  • Including decimals or fractions, which do not count as whole numbers.

Relation to Other Concepts

The idea of whole numbers connects closely with topics such as Integers and Counting Numbers. Mastering this helps build a solid foundation for fraction, decimals, or even advanced topics like algebra and number theory.


Classroom Tip

A quick way to identify whole numbers is to ask: “Is the number negative?” or “Does it have a decimal or fraction part?” If the answer is no to both, it’s a whole number! Vedantu’s teachers often use a number line chart in class for this check.


Wrapping It All Up

We have explored whole numbers—from definition, comparison with natural numbers, key properties, and examples, to common mistakes. To master whole numbers, practice with lists, check your answers, and use visual tools like the number line. Keep building your math confidence with more live sessions and practice worksheets on Vedantu!


Competitive Exams after 12th Science
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FAQs on Whole Numbers: Meaning, Properties, and Examples

1. What are whole numbers in mathematics?

Whole numbers are the set of positive integers including zero. They can be represented as the set {0, 1, 2, 3, 4, ...} and continue to infinity. A key feature is that they do not include any fractions, decimals, or negative numbers. They are used for counting complete objects.

2. What is the key difference between whole numbers and natural numbers?

The main difference is the inclusion of zero (0). The set of whole numbers starts from 0 {0, 1, 2, 3,...}, while the set of natural numbers (also called counting numbers) starts from 1 {1, 2, 3,...}. Therefore, all natural numbers are whole numbers, but not all whole numbers are natural numbers.

3. Which is the smallest whole number, and why is it important?

The smallest whole number is 0 (zero). Its importance in mathematics is fundamental for several reasons:

  • It serves as the additive identity, meaning any number added to zero remains unchanged (e.g., 5 + 0 = 5).
  • It is the starting point or origin on the number line for representing whole numbers.
  • It acts as a placeholder in the place value system, helping to distinguish between numbers like 52 and 502.

4. What are the main properties of whole numbers with examples?

Whole numbers have several important properties that govern arithmetic operations:

  • Closure Property: The sum or product of two whole numbers is always a whole number (e.g., 4 + 5 = 9; 4 × 5 = 20).
  • Commutative Property: The order of numbers does not affect the result of addition or multiplication (e.g., 2 + 8 = 8 + 2; 2 × 8 = 8 × 2).
  • Associative Property: The way numbers are grouped does not change the outcome of addition or multiplication (e.g., (3 + 4) + 5 = 3 + (4 + 5)).
  • Distributive Property: Multiplication distributes over addition (e.g., 3 × (4 + 5) = (3 × 4) + (3 × 5)).
  • Identity Property: Adding 0 (additive identity) or multiplying by 1 (multiplicative identity) does not change a number's value (e.g., 7 + 0 = 7; 7 × 1 = 7).

5. How can whole numbers be shown on a number line?

On a number line, whole numbers are represented as distinct points starting from 0 and moving to the right at equal intervals. The line begins at 0, followed by 1, 2, 3, and so on, with an arrow at the end to show that the numbers continue infinitely. This visual tool helps in understanding addition, subtraction, and the order of numbers.

6. Why aren't fractions or decimals considered whole numbers?

Fractions and decimals are not considered whole numbers because they represent parts of a whole, not a complete unit. The definition of a whole number is based on counting entire, indivisible objects. For example, you can have 3 apples (a whole number), but if you have 3.5 apples, the '.5' part is a fraction, so 3.5 is not a whole number.

7. If all whole numbers are integers, why aren't all integers whole numbers?

This is because the set of integers includes all whole numbers and their negative counterparts (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...). The definition of whole numbers, however, is restricted to only non-negative numbers {0, 1, 2, ...}. Therefore, negative integers like -1, -5, and -100 are not whole numbers.

8. What are some examples of whole numbers in everyday life?

Whole numbers are used constantly in everyday situations. For example:

  • Counting the number of students in a classroom.
  • Measuring your age in complete years.
  • The number of pages in a book.
  • Counting the amount of money in your pocket as whole rupees or dollars (e.g., ₹10).

9. What happens when you divide any whole number by zero?

Division of any whole number by zero is undefined in mathematics. This is because division is the inverse of multiplication. For example, if we say 6 ÷ 0 = x, it would mean that x × 0 = 6. However, any number multiplied by 0 is 0, so no value of x can satisfy this equation. Therefore, it has no meaningful answer.

10. Does the closure property apply to the subtraction of whole numbers? Explain why.

No, the closure property does not apply to the subtraction of whole numbers. This property states that the result of an operation between two numbers in a set must also be in that same set. While adding or multiplying two whole numbers always results in a whole number, subtracting them does not. For example, 5 – 8 = -3. Here, 5 and 8 are whole numbers, but the result, -3, is a negative integer and not a whole number.