126 LearnersLast updated on July 25th, 2025
Difference Between Natural and Whole Numbers
The difference between whole number and natural numbers is the inclusion of zero (0) in the set of whole numbers. In mathematics, numbers are classified into different categories: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, and Complex Numbers. In this article, we will learn about the difference between Natural and Whole Numbers.
What are Natural Numbers?
Natural numbers always start from 1 and increase by one each time, such as 1, 2, 3, 4, and so on, continuing without end. The other name for natural numbers is counting numbers, as they are used for counting objects. A set of natural numbers is represented as:
N = {1, 2, 3, 4, 5, …}
What are Whole Numbers?
Whole numbers start from 0 and continue as 1, 2, 3, and so on. They are commonly used in everyday mathematical tasks such as counting and solving basic problems involving adding, subtracting, multiplying, or dividing. A set of whole numbers is written as:
W = {0, 1, 2, 3, 4, 5, …}
The Difference Between Natural and Whole Numbers
In mathematics, natural and whole numbers are fundamental concepts. Natural and whole numbers have similarities, but they also differ in some ways. In this section, we will learn the difference between natural and whole numbers.
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Natural Numbers |
Whole Numbers |
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The natural numbers are the counting numbers that begin with 1 and go on endlessly, such as 1, 2, 3, and so on. |
The whole numbers can be defined as the positive numbers, including 0. |
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A set of natural numbers is represented by the letter N. |
A set of whole numbers is represented by the letter W (sometimes as N0). |
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The natural numbers do not include 0 in their set. |
The whole numbers include 0 in their set. |
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The smallest natural number is 1. |
The smallest whole number is 0. |
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Natural numbers are a subset of whole numbers. |
Whole numbers are the superset of natural numbers. |
| The set of natural numbers is {1, 2, 3, 4, 5, …}. |
The set of whole numbers is {0, 1, 2, 3, 4, 5, …}. |
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They are used for counting objects. |
They are used for measuring quantities that include zero. |
Real-Life Applications of the Difference Between Natural and Whole Numbers
The concepts of natural numbers and whole numbers are used in various real-life situations, such as counting objects, measuring scores, and representing empty numbers.
Sports Ranking and Scores:
While ranking the players in a tournament, positions like 1st, 2nd, 3rd are used. There is no mention of 0th place. We use natural numbers for rankings. When it comes to scoring in some sports, a team can have 0 points at the beginning of a game. In this case, we use whole numbers to represent the score, since whole numbers include 0.
Programming and Indexing:
In some situations, like making a numbered list, the count often starts from 1, which is based on natural numbers. In the most programming languages, arrays and lists start counting from 0. This is called zero-based indexing, where whole numbers are used to represent each position in the list.
Phone Number Digits:
Phone numbers consist of digits and may begin with 0. However, in some countries, area codes or country codes begin with 0. For example, a number like 0987432413 starts with a leading zero, showing that 0 can be useful. Here, whole numbers are used to write the country codes.
Common Mistakes and How to Avoid Them in the Difference Between Natural and Whole Numbers
When children mention the differences between natural numbers and whole numbers, they may make mistakes. Let us make it easier for children to understand this topic clearly by pointing out common mistakes they make and guiding them with simple explanations and solutions.
Mistake 1
Forgetting That 0 is a Part of Whole Numbers
Children may think that whole numbers also start with 1, like natural numbers. For example, when they try to write a list of whole numbers, they may start with 1 instead of 0. Children should be taught that the set of whole numbers begins with 0, while the set of natural numbers starts with 1.
Mistake 2
Thinking Whole Numbers Include Negative Numbers
Students often make mistakes in considering negative numbers as a subset of whole numbers. For example, considering -1, -2, or -9 belong to the set of the whole numbers. Students should be taught that whole numbers always exclude negative numbers.
Mistake 3
Believing 0 Has No Value
Students often think 0 as valueless. 0 is a number just like any other number used for marking place values and calculations.
Mistake 4
Getting Arithmetic Operations Wrong
When it comes to arithmetic operations, children may believe that all arithmetic operations always result in whole numbers. For example, 4 - 8 does not result in a whole number. It gives a negative result, -4, which is an integer and does not belong to the set of whole numbers. To avoid such mistakes, children should know about the properties of whole numbers.
Mistake 5
Representing Incorrect Number Lines
Children may draw number lines incorrectly when it comes to whole numbers and natural numbers. For example, they may start the number line of whole numbers from 1, instead of 0. Children should know the definitions of whole numbers and natural numbers properly, which helps them to draw number lines correctly.
Solved Examples of Difference Between Natural and Whole Numbers
Problem 1
The bank accounts balance of Rahul is zero. Does it belong to natural numbers or whole numbers?
0 belongs to whole numbers.
Explanation
The natural numbers start from 1, and the whole numbers include 0. So, the bank balance belongs to whole numbers.
Problem 2
What is the sum of the first five natural numbers?
1 + 2 + 3 + 4 + 5 = 15.
Explanation
The first five natural numbers are 1, 2, 3, 4, and 5. When we add them together, we will get 15 as their sum.
Problem 3
A train starts at station 0 and reaches station 8. Which number set is used for station numbering?
The whole number set is used for station numbering.
Explanation
Since 0 is included in the station numbering, it follows the whole number system.
Problem 4
Are whole numbers and natural numbers closed under multiplication?
Yes, both whole numbers and natural numbers are closed under multiplication.
Explanation
Multiplying two natural numbers always gives another natural number. For example, 2 × 4 = 8, and 8 is also a natural number. Similarly, when you multiply two whole numbers, the result is still a whole number. For example, 2 × 0 = 0, and 0 is a whole number.
Problem 5
Identify the natural numbers and whole numbers from the list given below 4, 3, - 45, 120, 0, 0.45
The natural numbers are 4, 3, and 120. The whole numbers are 4, 3, 120, and 0.
Explanation
As we know that all the positive numbers starting from 1 are natural numbers. The positive numbers, including 0, are whole numbers.
FAQs on the Difference Between Natural and Whole Numbers
1.Is every natural number a whole number?
2.What are the first five whole numbers?
3. What is the smallest whole number?
4.Do whole numbers include negative numbers?
5. What is the main difference between natural numbers and whole numbers?
6.How can children in United Arab Emirates use numbers in everyday life to understand Difference Between Natural and Whole Numbers ?
7.What are some fun ways kids in United Arab Emirates can practice Difference Between Natural and Whole Numbers with numbers?
8.What role do numbers and Difference Between Natural and Whole Numbers play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Difference Between Natural and Whole Numbers skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
