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Natural Whole Integer Real Rational Irrational Numbers

Natural Number

Any number that matches to a number from 1, 2, 3, 4, …. is called a natural number or counting number.

Example

4, 9 , 11, 35, 99, 500 or 9876 are natural numbers.

Natural numbers are used for counting and ordering. On the basis of that they can be further divided into cardinal and ordinal numbers.

1. Cardinal numbers

Cardinal numbers are used for counting of objects. For example, there are 7 apples in a box or there are 7 days in a week. In both examples, we are counting objects which are 7.

2. Ordinal numbers

Ordinal numbers are used to order the positions of objects or in other words, we can tell the position of an object.

Example

Example 1
Ist position or 2nd position and so on. The example of ordinal numbers is, girls stood Ist in the race.
Example 2
This is the second largest country in the world.

Note

Set of natural numbers is denoted by N.

Whole Number

Any number that matches to a number from 0, 1, 2, 3, 4, …. is called a Whole Number.

Example

0, 2, 14 , 23, 48, 172, 623 or 1245 are whole numbers.

Note

Set of whole numbers is denoted by W.

Integers

All natural numbers and negative of natural numbers including zero are called Integers. It includes 0 and all negative numbers and positive natural numbers.

Example

-65, -12, -5, 0, 56, 89 or 354 are Integers.

Also, the negative numbers are additive inverse of positive corresponding numbers.
What are additive inverse? Additive inverse refers to the sum of a positive number and corresponding negative number is equal to 0.

Example

2 is additive inverse of -2.
Because -2 + 2 = 0.

Note

Zero is neither a negative number nor positive number. It is a neutral number.
Set of integers is denoted by Z.

Rational Numbers

The numbers each of which can be expressed in the form of pq , where p and q are integers and q is not equal to zero, are called Rational Numbers.
Besides, the rational numbers are also non terminating and repeating numbers.

Example

25 , 13 , 89 , 310 etc.

Note

Set of rational numbers is denoted by Q.
Rational number is also a real number.

Irrational Numbers

The numbers which are not rational are called irrational numbers. Besides, irrational numbers are also non terminating and non repeating numbers.

Example

2 , 5 etc.

Real Numbers

Set of rational numbers and irrational numbers is called Real Numbers. In other words, real numbers include all rational and irrational numbers.

Example

7 , 18 , 310 etc.

All real numbers can be represented on a number line which is also called a real line.

Note

Set of real numbers is denoted by R.

Worksheet on Types of Numbers

Fill in the blanks

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natural
1
position
neutral number
integers
real
repeating
irrational
zero
-7

1) The numbers those start with 0, 1, 2 are called ___________ numbers.

2) The first natural number is ___________.

3) Rational and irrational numbers taken together are called ___________ numbers.

4) The rational numbers are non terminating and ___________ numbers.

5) π is an ___________ number.

6) In rational number p q , q must not be equal to ___________.

7) Additive inverse of 7 is ___________.

8) Zero is a ___________ number.

9) All positive numbers and negative numbers together are called ___________.

10) Ordinal numbers are used to tell the ___________ of an object.