Difference Between Natural Numbers and Whole Numbers
The main difference between natural numbers and whole numbers is related to the number 0 which is only a part of the set of whole numbers and is not present in the set of natural numbers. One of the most important aspects of mathematics is numbers. We need numbers to count, measure, and label. These can be presented in different forms such as digits, words, and on a line. Numbers are those values that represent a particular quantity. In mathematics, numbers are of different types - Natural Numbers, Whole Numbers, Integers, Real Numbers, Rational Numbers, Irrational Numbers, and Complex Numbers.
In this article, we are going to learn the definition of natural numbers, the definition of whole numbers, and the difference between natural numbers and whole numbers with examples.
1. | What are Natural Numbers? |
2. | What are Whole Numbers? |
3. | Difference between Natural Numbers and Whole Numbers |
4. | FAQs |
What are Natural Numbers?
Natural numbers are also known as counting numbers because these numbers can be counted on our hands. For example, the numbers that we count on our hands are 1, 2, 3, 4, 5, 6, and so on. By definition, natural numbers are a part of the number system that includes only positive integers from 1 and that can be counted on our hands. The number 1 is considered to be the smallest natural number. Therefore, 0, negative numbers, fractions, and decimals are not considered to be natural numbers. A few examples of natural numbers are 46, 72, 25, 888, 560, etc.
What are Whole Numbers?
Whole numbers are those numbers that include positive integers along with 0. These are represented on the right side on a number line. 0 is considered as the smallest whole number. It is to be noted that positive integers and natural numbers are also considered as whole numbers, whereas, fractions and decimals do not come under whole numbers. Arithmetic operations like addition, subtraction, multiplication, and division are possible on whole numbers. A few examples of whole numbers are 0, 15, 37, 97, 67, etc.
Difference between Natural Numbers and Whole Numbers
The basic difference between natural numbers and whole numbers is that natural numbers do not include the number 0 and here the smallest number is 1. Whereas, whole numbers include 0, and here the smallest number is 0. Observe the figure given below which shows the difference between the set of natural numbers and whole numbers.
Natural numbers vs Whole Numbers
The following table shows the difference between natural numbers and whole numbers.
Natural Numbers | Whole Numbers |
---|---|
Natural numbers are counting numbers beginning with the number 1. | Whole numbers are natural numbers that begin with the number 0. |
All positive integers are included in the set of natural numbers. | All positive integers and zero are included in the set of whole numbers. |
All natural numbers are considered as whole numbers. | All whole numbers are not considered natural numbers. |
Represented by the letter 'N'. | Represented by the letter 'W'. |
Natural numbers are closed under addition and multiplication. | Whole numbers are closed under addition and multiplication. |
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Examples on Difference between Natural Numbers and Whole Numbers
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Example 1: Identify whole numbers from the given numbers: 7/9, 0, 7, 69.6, 10, -21, -56, 90
Solution: From the given list, the whole numbers are 0, 7, 10, and 90
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Example 2: "Every whole number is also a natural number." Is this statement true? Justify your answer.
Solution: No, every whole number is not a natural number. By definition, natural numbers are a part of the number system that contains all positive integers starting from the number 1 to infinity. Whereas, whole numbers include all positive numbers starting from the number 0 to infinity. The number 0 is a whole number but not a natural number. Therefore, we can say that natural numbers contain all the whole numbers except the number 0. Therefore, the statement, every whole number is also a natural number is not true.
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Example 3: Identify whole numbers and natural numbers from the given list 4.5, 121, 56/90, 4, -79, 0, 30
Solution: The difference between natural numbers and whole numbers is that natural numbers include all positive integers without 0 and whole numbers include positive integers along with 0. From the given list,
- The whole numbers are 121, 4, 0, 30
- The natural numbers are 121, 4, 30
Practice Questions on Difference between Natural and Whole Numbers
FAQs on Difference between Natural Numbers and Whole Numbers
What is the Difference between Natural Numbers and Whole Numbers?
Natural numbers are those numbers that include only positive integers starting from 1 and they go on till infinity. Whereas, whole numbers are those numbers that include 0 and natural numbers, begin from 0 and go on till infinity.
Are Natural Numbers and Whole Numbers the same?
Natural numbers begin from the number 1, whereas, whole numbers begin from 0. All natural numbers are considered to be whole numbers but all whole numbers are not considered to be natural numbers.
Which Number is not common between Natural and Whole Numbers?
The number which is not common between natural numbers and whole numbers is 0. This means that whole numbers include 0 but natural numbers do not.
Are Integers Whole Numbers or Natural Numbers?
Integers include whole numbers and natural numbers. The numbers that are positive, negative and 0, are called integers. These numbers can be represented on a number line. All the positive numbers and 0 are the whole numbers. Fractions and decimals are not included in the list of whole numbers.
Are all Natural Numbers, Whole Numbers?
Yes, all the natural numbers are whole numbers since natural numbers begin from 1,2,3,4 and so on and whole numbers begin from 0, 1,2,3,4, and so on. But not all whole numbers are natural numbers.
What are the First Five Natural Numbers?
The first five natural numbers are 1, 2, 3, 4, and 5. Natural Numbers are the numbers that are used for counting and are a part of real numbers.
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