The cardinal numbers are the numbers that are used for counting something. These are also said to be cardinals. These are the natural numbers that start from 1 and goes on sequentially and are not fractions.
| The examples of cardinal numbers are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,…. |
The meaning of cardinals is ‘how many’ of anything is existing in a group. Like if we want to count the number of apples present in the basket, you have to make use of these numbers, such as 1, 2, 3, 4, 5….and so on. The numbers help us to count the number of things or people present in a place or a group. The cardinal numbers denote the collection of all the ordinal numbers.
Definition
As we already discussed, the numbers which can be counted are the cardinals. It means all the natural numbers come in this category. Therefore, we can write the list of cardinal numbers as;
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ……, 50, 51, 52, 53, 54, …., 99, 100, 101, 102, 103, 104, 105, ……, 999, 1000,…..,∞ |
So, with the help of these numbers given in the table above, we can define the counting of the objects or persons or animals or other things.
Cardinal Examples
The cardinality of a group represents the number of objects available in that group.
- There are 6 clothes in the cupboard.
- 4 cars are driving in a lane.
- Anusha has 2 dogs and 1 cat as pets in her house.
In the above three examples, the numbers 6, 4, 2 and 1 are the cardinal numbers. So basically it denotes the quantity of something, irrespective of their order. It defines the measure of the size of a set but does not take account of the order.
The set of finite numbers are the natural numbers that define cardinality. Whereas, the set of infinite cardinals describes the size of infinite sets. The cardinals don’t have any fractions or decimals; they have only counting numbers.
Cardinal Numbers of a Set
The number of elements or members in a set is the cardinal number of that set. If A is a finite set and it has elements equal to N. Then the cardinal number of set A is N.
Note: The cardinal number of an empty set is always zero.
For example, set A = {1, 3, 6, 9, 10, 12, 18}, the cardinal number of set A is 7. Hence, n(A) = 7
Thus, the only formula for counting numbers is to find the number of elements of any set.
Cardinal Numbers in English
Cardinal numbers define how many things or people are there. For example:
- Five men are standing on a ship.
- There eight fruits kept in a basket.
These numbers are written in English in the same way, and we write numbers in words. For the first 10 numbers, we can write here:
- 1-One
- 2-Two
- 3-Three
- 4-Four
- 5-Five
- 6-Six
- 7-Seven
- 8-Eight
- 9-Nine
- 10-Ten
Ordinal Numbers
The ordinal numbers are the numbers which denote the position of something. If several objects are mentioned in a list, the order of the objects is defined by ordinal numbers. The adjective terms which are used to denote the order of something are 1st, 2nd, 3rd, 4th, 5th, 6th, and so on.
Examples:
- Anil came to 3rd position in a running competition.
- The 6th chair is broken in a hall.
Cardinal and Ordinal Numbers Chart (1-100)
Let us create a chart table where we will write the cardinal numbers and equivalent ordinal numbers.
| Cardinals | Ordinals | Cardinals | Ordinals |
| 1, One | 1st, First | 11, Eleven | 11th, Eleventh |
| 2, Two | 2nd, Second | 12, Twelve | 12th, Twelfth |
| 3, Three | 3rd, Third | 13, Thirteen | 13th, Thirteenth |
| 4, Four | 4th, Fourth | 14, Fourteen | 14th, Fourteenth |
| 5, Five | 5th, Fifth | 15, Fifteen | 15th, Fifteenth |
| 6, Six | 6th, Sixth | 16, Sixteen | 16th, Sixteenth |
| 7, Seven | 7th, Seventh | 17, Seventeen | 17th, Seventeenth |
| 8, Eight | 8th, Eighth | 18, Eighteen | 18th, Eighteenth |
| 9, Nine | 9th, Ninth | 19, Nineteen | 19th, Nineteenth |
| 10, Ten | 10th, Tenth | 20, Twenty | 20th, Twentieth |
After 20, the denotation or pattern of Ordinal numbers changes as;
| 21, Twenty-One | 21st, Twenty-First | 26, Twenty Six | 26th, Twenty-Sixth |
| 22, Twenty-two | 22nd, Twenty-second | 27, Twenty Seven | 27th, Twenty-Seventh |
| 23, Twenty-three | 23rd, Twenty-third | 28, Twenty Eight | 28th, Twenty-Eighth |
| 24, Twenty-four | 24th, Twenty-fourth | 29, Twenty Nine | 29th, Twenty-Ninth |
| 25, Twenty-five | 25th, Twenty-fifth | 30, Thirty | 30th, Thirtieth |
In the same way, we can write the numbers till infinity following the same order, after 30 or 30th.
To practice, students can write the ordinals after numbers such as 40, 50, 60, 70, 90, 100, as per given below;
| Cardinals | Ordinals |
| 40, Forty | 40th, Fortieth |
| 50, Fifty | 50th, Fiftieth |
| 60, Sixty | 60th, Sixtieth |
| 70, Seventy | 70th, Seventieth |
| 80, Eighty | 80th, Eightieth |
| 90, Ninety | 90th, Ninetieth |
| 100, Hundred | 100th, Hundredth |
Cardinal Numbers 100 to 1000
| 100 | One hundred |
| 200 | Two hundred |
| 300 | Three hundred |
| 400 | Four hundred |
| 500 | Five hundred |
| 600 | Six hundred |
| 700 | Seven hundred |
| 800 | Eight hundred |
| 900 | Nine hundred |
| 1000 | One thousand |
More:
| 10,000 | Ten Thousand |
| 100,000 | One hundred thousand |
| 1,000,000 | One million |
| 10,000,000 | Ten million |
Nominal Numbers
The nominal numbers are used to name an object or a thing in a set of group. It is used for the identification of something. It is not for representing the quantity or the position of an object.
Examples:
- Model numbers of Vehicles.
- Pincodes of various cities.
Related Links:-
| Decimal Numbers Standard Form | Difference Between Natural And Whole Numbers |
| Estimation Of Numbers | Introduction To Large Numbers |
Frequently Asked Questions – FAQs
What is a cardinal number? Give example.
Example: there are 5 flowers in a vase, then 5 shows the cardinality of flowers.
