[Maths Class Notes] on Difference Between Natural and Whole Numbers Pdf for Exam

There are various types of numbers, such as Whole Numbers, Natural numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. And more often than not students may find it confusing, that is to say, the student may confuse one with the other. Especially in the natural numbers and the whole numbers, because both of them kind of seem similar. And therefore, it is important for the students to have a clear understanding of the Whole number and the Natural numbers.

Understanding Whole Numbers

Before diving deep into the difference between the Whole numbers and Natural numbers, it is important for the students to first understand, both the terms, Whole Numbers and Natural numbers separately. Because the main difference between the two lies in their meaning. Therefore, let us start with the Whole Numbers.

You may be familiar with the term integers, if not, here is a quick review. Integers are those numbers that can be expressed without the use of fractions, in short numbers which are not a fraction are integers. For example numbers 1, 25, 124, 5624, -54 are all integers because they do not require fractions. But the numbers ¾, ½ are not integers, because they are expressed in a fraction.

Now, coming to the whole numbers, all the positive integers along with the 0 are called whole numbers. It means decimals such as 5.2, 3.2; Negatives, such as -5, -6; and the fractions are not the whole numbers. 

If you wish to learn more about the whole numbers you may like to follow this link.

Understanding Natural Numbers

Now, coming to the natural numbers, it is just as simple as Whole numbers. Because all you have to do is to remove the 0 from the whole numbers and you have got natural numbers. Yes, all the positive integers of the number system are called natural numbers. It means integers such as 1, 5, 8, 541, etc are all natural numbers. But just like the whole numbers here again the decimals, negatives, and fractions are not included. You can vaguely say all the numbers that we commonly use for counting are Natural Numbers

Difference Between Natural Numbers and Whole Numbers

 

Life without numbers is unimaginable. There are numerous properties of numbers that led to their categorization. The most primary thing to note is that all natural numbers are whole numbers. However, there are other categories of numbers such as

• Whole Numbers

• Natural Numbers

• Integers

• Rational Numbers

• Irrational Numbers

• Real Numbers

• Complex Numbers

These categories differ from each other by their properties. Let’s explore the differences between Natural and Whole numbers.

0 is the smallest whole number. In mathematics, the most basic set is that of whole numbers. These whole numbers are an integral part of the real number set which comprises various other number sets like integers, rational numbers among others.

 

Except 0, every whole number has exactly one immediate predecessor that is the number that comes before a whole number.  Every whole number has exactly one immediate successor that is the number that comes after a whole number.

 

The basic difference between natural numbers and whole numbers is that the whole numbers set include 0 Instead natural numbers set doesn’t include 0. Let us talk about other differences as shown below.

 

Difference Between Natural and whole Numbers

Whole Number

• All Whole numbers are represented by ‘W’

• In whole numbers counting starts from ‘0’ ZERO

• When 0 is added to a number the answer is just the number you start with: 24+0=24.

• For this reason, 0 is called the identity element for addition. The identity element is absent from the natural numbers for additional property.

All whole numbers are also integers. For each whole number, there is a negative number that corresponds with it. For instance, -5 corresponds to the whole number 5, and -120 corresponds to the whole number 120.

 

Within the set of integers, the sum of two numbers can be 0.

 

For eg. 20+(−20)=0 and 135+(−135)=0.

 

20 and -20 will be termed as the additive inverses.

 

Natural Number

• All Natural numbers are represented by ‘N’

• In natural numbers counting starts from ‘1’

• When you add two or more natural numbers, you get a natural number again.

• When you multiply two or more natural numbers, you get a natural number again

The maths way to
say it is that “The system of natural numbers is closed under addition and multiplication”. It means that when subtraction or division is performed on natural numbers the result may not always be a natural number.

 

Examples of Whole Numbers and Natural Numbers

Example 1. Find whole numbers from given numbers. 14,0,8,48,-6,-9,2

Sol. Whole numbers: 14,0,8,48,2

 

Example 2. Find natural numbers from given numbers.

24,(0.6),6,40,-60,0,-2

Sol. natural numbers: 24,6,40

 

Explanation of Addition Property of Natural and Whole Numbers

When two natural numbers are added, it results in a natural number only. 

 

Eg: 34+45 = 79

 

Adding two whole numbers will give you a whole number. 

 

Eg: 6+0= 6

 

Explanation of Subtraction Property of Natural and Whole Numbers

Subtraction of two natural numbers doesn’t necessarily result in a natural number

 

Eg: 8 – 5 = 3 is a natural number 

 

But 5 – 8 = -3 is not a natural number

 

Similar is the condition for whole numbers. Subtracting two whole numbers need not result in a whole number.

 

Explanation of Multiplication Property of Natural and Whole Numbers

Multiplication of a natural number with a natural number and a whole number with another whole number results in a natural number and whole number respectively.

 

Eg: 4 x 3 = 12 is a natural number

 

8 x 5 = 40 is a whole number, where 8 and 0 are also whole numbers.

 

Explanation of Division Property for Natural and Whole Numbers

Division property also does not hold for the natural numbers and whole numbers for instance.

 

Eg: 10/2 = 5 is natural as well as the whole number

 

But 7/2 = 3.5 is neither natural nor the whole number.

 

Similarly, the difference between natural numbers and whole numbers can be understood by representing them on a number line.

 

Whole numbers are located on the right side of the number line including zero.

 

Natural numbers are located on the right side excluding zero.