Cardinal Number
Cardinal numbers are numbers that are used for counting. They are also known as natural numbers or cardinals. A set of cardinal numbers starts from 1 and it goes on up to infinity. We use cardinal numbers to answer the question "how many?". For example, how many students are going to the school picnic? The answer could be any number like 20, 23, 30, etc. So, all these numbers come in the category of cardinal numbers. In this article, we will explore the world of cardinal numbers and understand the difference between cardinal and ordinal numbers.
What are Cardinal Numbers?
A Cardinal Number describes or represents how many of something are present. Example 2 apples, 5 flowers, etc. It quantifies an object. It does not have values as fractions or decimals. Cardinal numbers are counting numbers, they help to count the number of items. Let's have a look at cardinal numbers examples. Ana wants to count the number of people standing in a queue at a billing counter. Can you help her? Ana started to count using Natural numbers.
Ana counted 1, 2, 3, 4, and 5. There are 5 people standing in a queue at the billing counter. Counting numbers are cardinal numbers! Now, Let's consider another example, Noah kept eight apples in a basket. The number eight denotes how many apples are there in the basket, irrespective of their order.
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, 21, and so on. The smallest Cardinal number is 1 as 0 is not used for counting, so it is not a cardinal number.
Difference Between Cardinal and Ordinal Numbers
All the natural numbers are also referred to as cardinal numbers. Cardinal numbers are used for counting. While an ordinal number is a number that denotes the position or place of an object. Example: 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, 5^{th}, etc. Ordinal numbers are used for ranking. Here is an example that explains Cardinal and Ordinal Numbers:
In the above image, we can see a team of 4 workers on the construction site. This is an example of cardinal numbers.
In the above image, we can see the position of the runners in the running event. First, second, third, and so on. This is an example of ordinal numbers. Let's discuss ordinal and cardinal number differences in the table below:
Cardinal Numbers  Ordinal Numbers 

They are counting numbers that represent quantity.  They are based on the rank or position of an object in a given list or order. 
Cardinal numbers give us the answer of 'how many?'.  Ordinal numbers give us the answer of 'where'. For instance, where does the object lies in the list? 
Examples are 1, 2, 3, 4, 5, 10, etc.  Examples are 1^{st}, 2^{nd}, 3^{rd}, 4^{th}, 5^{th}, 10^{th}, etc. 
List of Cardinal Numbers from 1 to 100
Given below are the basic and most important cardinal numbers, which form the base for other counting numbers.
1  One  6  Six 
2  Two  7  Seven 
3  Three  8  Eight 
4  Four  9  Nine 
5  Five  10  Ten 
10  Ten  60  Sixty 
20  Twenty  70  Seventy 
30  Thirty  80  Eighty 
40  Forty  90  Ninety 
50  Fifty  100  Hundred 
Given below is the list of all cardinal numbers from 1 to 100. It will also help you to see how we write cardinal numbers in words like 21 twentyone.
Cardinal Numbers of a Set
In the case of a set, the cardinal number is the total number of elements present in it. In other words, the number of distinct elements present in a set is the cardinal number of the set. The cardinal number of a set A is represented as n(A). For example, the cardinal number of set W = {1, 3, 5, 7, 9} is n(W)=5, as there are 5 elements in it.
Think Tank:
 Maria wrote January 1, 2020, as today’s date in her notebook. Does the number 1 in the date, represent a cardinal number?
 There are _______ people in the line ahead of me. I am the 7th person in the line.
Important Notes:
 Cardinal numbers help us to count the number of things or people in or around a place or a group.
 The collection of all the ordinal numbers can be denoted by the cardinal.
 Cardinal numbers can be written as words such as one, two, three, etc.
 Cardinal numbers tell how many items, whereas ordinal numbers show position or ranking.
Cardinal Numbers Related Articles
Check out these interesting articles to know more about cardinal numbers and its related articles.
Solved Examples on Cardinal Numbers

Example 1: Kate has a list of numbers as shown  7, 8^{th}, 10, Two, Fourth, 2^{nd}. Identify the cardinal numbers.
Solution:
7, 10 and two help us in counting, whereas 8^{th}, fourth and 2^{nd} helps us in identifying the position. Thus, 7, 10, and two are cardinal numbers.

Example 2: Help Ryan, to calculate the number of vowels in "NUMBERS". Also, identify the number of alphabets used to form this word.
Solution:
(i) We know that a, e, i, o, and u are the vowels and in the given word u and e are used. Therefore, 2 vowels are used to form this number (2 is the required cardinal number).
(ii) We start counting from N to S, we see that "Numbers" has 7 alphabets in all. Therefore, a total of 7 alphabets are required to form the given word and here 7 is a cardinal number.
FAQs on Cardinal Numbers
What is a Cardinal Number Example?
Cardinal numbers are used for counting. Some examples of cardinal numbers are 1, 2, 3, 4, 5, 10, 15, 20, 30, 40, 50, 100, etc. In our daily life, we use cardinal numbers a lot. Even a small child uses this mathematical concept without knowing the term for it. They do count how many toys they have, how many people are there around them, how many friends they have, how many subjects do they study at school, etc.
What is the Smallest Cardinal Number?
The smallest cardinal number is 1 (one) as whenever we count, we always start from 1.
How do you Find Cardinal Numbers?
Cardinal numbers can be found by counting. We start by 1 and then go on as per the number sequence.
How is Cardinal Number Different from the Ordinal Number?
Cardinal numbers are numbers that represent the number of items(quantity) while ordinal numbers represent the rank or position of an item in the given list.
What is a Cardinal Number in Sets?
In set A, if there are a total of 25 elements then 25 is the cardinal number of set A represented by n(A).
Can Cardinal Numbers Negative?
No, cardinal numbers cannot be negative. They are positive integers or natural numbers, as we always count the number of items starting from number 1, and then it goes up to infinity.
Is Zero a Cardinal Number?
No, 0 is not a cardinal number as cardinal numbers represent quantity, and 0 means nothing or no quantity.
What is the Biggest Cardinal Number?
There are infinite natural numbers. Therefore, there are as many cardinal numbers as natural numbers. There can be no generalization of the biggest natural number and so does for the biggest cardinal number.
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