Difference Between Natural and Whole 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 in digits, in 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.
The main difference between natural and whole numbers is the number 0 which is only a part of the set of whole numbers and not in natural numbers. In this article, we are going to learn the definition of natural numbers, the definition of whole numbers, and the difference between natural and whole numbers with examples.
|1.||Definition of Natural Numbers|
|2.||Definition of Whole Numbers|
|3.||What is the Difference between Natural and Whole Numbers?|
Definition of Natural Numbers
Natural numbers are also known as counting numbers as these numbers we can count on our hand. 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 the smallest natural number hence 0, negative numbers, fractions, and decimals are not considered natural numbers. Examples of natural numbers are 46, 72, 25, 888, 560, etc.
Definition of Whole Numbers
A part of the number system, 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, positive integers, and natural numbers are also considered as whole numbers. Whereas, fractions and decimals do not come under the whole number bracket. Arithmetic operations like addition, subtraction, multiplication, and division are possible on whole numbers. Examples of whole numbers are 0, 15, 37, 97, 67, etc.
What Is the Difference between Natural and Whole Numbers?
One of the basic and main differences between natural and whole numbers is that natural numbers do not include the number 0 and have the smallest number as 1. Whereas, whole numbers include 0 and have the smallest number as 0. Listed below are a few more differences between natural and whole numbers.
Natural numbers vs Whole Numbers
|Natural Numbers||Whole Numbers|
|Natural numbers are counting numbers beginning with the number 1||Whole numbers are natural numbers but beginning with the number 0|
|All non-zero integers are included in the natural numbers set.||All positive integers are included in the whole numbers set.|
|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.|
Listed below are a few topics that are related to the difference between natural and whole numbers.
Solved Examples on Difference between Natural and Whole Numbers
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
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, a whole number includes all positive numbers starting from the number 0 to infinity. The number 0 is a whole number but not a natural number. But 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.
Example 3: Identify whole numbers and natural numbers from the given list 4.5, 121, 56/90, 4, -79, 0, 30
Solution: From the given list,
- The whole numbers are 121, 4, 0, 30
- The natural numbers are 121, 4, 30
FAQs on Difference between Natural and Whole Numbers
What is the Difference between Natural Numbers and Whole Numbers?
Natural numbers are those numbers that include only positive integers and begin from 1 till infinity. Whereas, whole numbers are those numbers that include 0 and natural numbers, begin from 0 and end at infinite value.
Are Whole Numbers and Natural Numbers the same?
Natural numbers begin from the number 1. Whereas, whole numbers begin from 0. Natural numbers are considered as whole numbers but not vice versa. Whole numbers include natural numbers after it begins with 0.
Which Number is not common between Natural and Whole Numbers?
The main difference between natural and whole numbers and the number which is not common is the number 0. Whole numbers include 0 but natural numbers do not.
Are Integers Whole Numbers or 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.