Cardinal numbers definition

What are Cardinal Numbers? Definition, List, Examples, Facts

What Are Cardinal Numbers?

Cardinal numbers are numbers that are used for counting real objects or counting things. They are also known as “counting numbers” or “cardinals.” We commonly use cardinal numbers or cardinals to answer the question starting with “How many?”

So, how to find the cardinal numbers around us? Let’s see an example.

Example:

How many dogs are in the given picture?

To know the total number of dogs, we need to count the dogs given in the image.

There are 8 dogs in all. Here, 8 is the cardinal number.

Related Games

Cardinal Numbers: Definition

The numbers that we use for counting are called cardinal numbers. They tell us the quantity of objects.

Cardinal Numbers Examples: 2 bananas, 5 suitcases, 100 points, a million dollars, etc.

Cardinal numbers do not include fractions or decimals. Cardinal numbers are natural numbers or positive integers. The smallest cardinal number is 1.

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.

If we count a bag filled with a million dollars, we get a cardinal number: “one million!”

Example:

Related Worksheets

Cardinal Numbers in Words

We can also write cardinal numbers in words. For the first 10 numbers, we can write the cardinal numbers as:

1 – One
2 – Two
3 – Three
4 – Four
5 – Five
6 – Six
7 – Seven
8 – Eight
9 – Nine
10 – Ten

List of Cardinal Numbers

Here’s a list of cardinal numbers up to 100, in figures and in words:

Cardinal Numbers as Multiples of 100:

We can count further and list a few larger cardinal numbers as well:

What Is Cardinality?

The cardinality of a group or a set represents how many elements or numbers are present in a group or in a set.

For example, if a pencil set has 10 pencils in it, then the cardinality of pencils is 10.

Cardinal Number of a Set

The number of elements in a set is known as the cardinal number of that set. If A is a finite set and it has N elements, then the cardinal number of set A is given by n(A) $=$ N.

Note: The cardinal number of an empty set is always zero.

For example, what is the cardinal number of a set if the set is defined as A $=$ {2, 5, 7, 9, 11, 15, 19, 22, 24}?

The cardinal number of set A is 9. Hence, n(A) $=$ 9

Cardinal Numbers vs. Ordinal Numbers

As we discussed, the cardinal numbers are used for counting. They include all the natural numbers. However, an ordinal number is a number that is used to represent the position or order of an object. Examples:

1^strank, 2^nd in a queue, 3^rd row, tenth floor, etc.

Ordinal numbers are used for ranking or ordering.

Here’s an example that explain the difference between cardinal and ordinal numbers:

In the image given above, we can see a group of 8 children on the picnic spot. Here, 8 represents the cardinal number.

In the above image, we can see the position of the kids in a running event. Here, first, second, third, fourth, fifth are ordinal numbers.

Difference between Cardinal Numbers and Ordinal Numbers

Nominal Numbers

Nominal numbers, as the name suggests, are used to name an object or a thing in a set of groups. They help us in the identification of objects. It is not used to represent the quantity or the position of an object.

For example:

Social security number
Zip code number
Cell phone number

In the image given below, the numbers 22, 18 are nominal numbers since they are used on the jerseys to represent players or to identify players.

Conclusion

In this article, we learnt about the Cardinal Numbers. Cardinal Numbers are the numbers used for counting numbers. To read more such informative articles on other concepts, do visit SplashLearn. We, at SplashLearn, are on a mission to make learning fun and interactive for all students.

Solved Examples

1. Kathy has a list of numbers as shown: 10, 9, 7^th, 22, Third, Five, 21^st. Identify the cardinal numbers.

Solution: The cardinal numbers are used for counting. The cardinal numbers are 10, 9, 22 and Five.

2. Help Mark calculate the number of consonants in “INDEPENDENCE.” Also identify the number of alphabets used to form this word.

Solution: The consonants are alphabets other than vowels. The vowels are a, e, i, o and u. The number of consonants INDEPENDENCE are 7. The number of alphabets in the word INDEPENDENCE are 12.

3. Write the cardinality of the flowers in the vase.

Solution: There are 5 flowers in the vase. So, the cardinality is 5.

4. What is the position of the strawberry from the left?

Solution: The strawberry is at the second position from the left. Here, second is the ordinal number.

5. How many kites are there in all? What is a cardinal number here?

Solution: On counting, we get:

There are 8 kites. 8 is the cardinal number since we used it for counting.

Practice Problems

How many two-digit numbers are there?

Correct answer is: 90
The smallest two-digit number is 10 and the greatest two-digit number is 99.
From 1 to 99, there are 99 numbers. Out of them 9 numbers (1 to 9) are one-digit numbers.
So, we will subtract 9 from 99 to find the two-digit numbers.
Number of two-digit numbers $= 99 – 9 = 90$

The cardinality of the set A $= {12, 18, 23, 65}$ is

Cannot be defined.

Correct answer is: 4
Since the number of elements in the set is 4, the cardinality of the set is 4.

Which of the following is not a cardinal number?

Sixty-one

4th

Correct answer is: 4th
4th is not a cardinal number as it tells us about the position of something.

For which of the following are cardinal numbers used?

To find the number of objects

To identify the rank or order of something

To identify objects

All of these

Correct answer is: To find the number of objects
We use cardinal or natural numbers for finding the number of objects.

76 is a $\underline{}$ number.

Ordinal

Cardinal

Nominal

None of these

Correct answer is: Cardinal
76 is a natural number and hence, it is cardinal.

Frequently Asked Questions

Which is the smallest cardinal number?

The smallest cardinal number is 1.

Can cardinal numbers be negative?

No, cardinal numbers cannot be negative. They are positive integers or natural numbers, as we count the number of items starting from number 1, and then it goes up to infinity.

Is 0 a cardinal number?

No, we can not count 0 things.

Which is the biggest cardinal number?

The biggest cardinal number is infinity.

Can we do operations with the cardinal numbers?

Yes, we can do operations with the cardinal numbers. We can add, subtract, multiply, and divide the cardinal numbers.

Are all whole numbers cardinals?

All whole numbers are not cardinal numbers. 0 is a whole number but not a cardinal number as we can never say that the number of objects is 0.

What is the Cardinal Counting Principle?

When you count a number of objects in a group, the total number of items is the last word said while counting.

Number
First
Ordinal Numbers

Cardinal Numbers - Meaning, Examples, Sets

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.

1.	What are Cardinal Numbers?
2.	Difference Between Cardinal and Ordinal Numbers
3.	List of Cardinal Numbers from 1 to 100
4.	Cardinal Numbers of a Set
5.	FAQs on Cardinal 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- twenty-one.

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.

Related Articles

Check out these interesting articles to know more about cardinal numbers and its related articles.

Ordinal Numbers
Whole Numbers
Natural Numbers
Difference Between Natural and Whole Numbers

Cardinal Numbers Examples

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.

go to slidego to slide

Breakdown tough concepts through simple visuals.

Math will no longer be a tough subject, especially when you understand the concepts through visualizations with Cuemath.

Book a Free Trial Class

Practice Questions on Cardinal Numbers

go to slidego to slidego to slide

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.

Cardinal numbers: digits, spelling. Numeral POL

Digits
Spelling of cardinal numbers
Soft sign in numerals
Numeral LOL
Syntactic role

Cardinal numbers are numerals denoting numbers and amounts of objects. Cardinal numbers answer the question how much? :

one, seven, one hundred and five .

Cardinal numbers change according to cases, but do not change according to numbers and genders. The exception is the numerals one, two, both, one and a half , which change by childbirth:

- one - one,

Two - two,

- both - both,

- one and a half 11;

and numerals one, thousand, million, billion , which change by numbers:

one - one,

thousand - thousand,

million - millions,

billion - billions .

Cardinal numbers are characterized by specific compatibility with nouns:

After the numeral one (one, one) nouns stand in the nominative singular :
one friend one cup , one case .
The numeral one is consistent with nouns in all cases:
one friend, one friend, one friend, one friend, about one friend .
After the numerals two, three, four nouns are in the genitive singular :
two friends , three bananas , four birches .
After all other numerals, nouns stand in the genitive plural :
seven friends , forty bananas , one hundred birches .
In all cases, except for the nominative, the numerals will agree with the nouns:
no two friends, approached two friends, proud of two friends, talked about two friends .

Digits

Cardinal numbers are divided into digits:

Integers (denoting an integer):
one, twenty-five, one hundred .

Fractional (denoting a fractional number):

three fifths, one eighth .

Fractional numbers consist of two parts: the first part is the numerator of the fraction is a cardinal number in the nominative case, the second part is the denominator of is the ordinal number in the genitive plural:

If the numerator is 1 or 2 , then the feminine form is used:

one tenth, two sevenths .

Fractional numbers are written separately.

In colloquial speech, some fractional numbers have specific names:

one second - half , one third - third , one fourth - quarter .

Nouns after fractional numbers are always put in the genitive singular:

half an apple, three fourths of the area, a quarter of a kilogram .

The word and a half also belongs to fractional numbers, which has only two forms:

Collective (total 11 pieces):

two, three, four, five, six, seven, eight, nine, ten ;

both (both, both), both (both).

Collective numerals denote the number of persons or objects as a single group, something united and inseparable:

two sisters, four friends .

Collective numbers combined:

With nouns that are used only in the plural:
two points, three sleds .
With masculine nouns denoting people and baby animals:
three friends, five kittens .
Regular quantitative nouns can also be combined with these nouns:
three friends - three friends, five kittens - five kittens .
With nouns denoting paired items:
two socks, three boots .
Only the numeral and both can be combined with feminine nouns:
both sisters, both legs .
With personal pronouns:
there will be six of us .

After the collective nouns in the nominative case, the noun is placed in the genitive plural :

two boys , three kittens , five boys .

After the collective numbers both, both , standing in the nominative case, the noun is put in the genitive singular :

both boys , both girls .

The numerals both, both are the only collectives that combine with any nouns denoting countable objects:

both windows, both cases, both doors, both legs .

Spelling of cardinal numbers

Cardinal numbers ending in -TEN, -STA, -COT , written together:

seventy, four hundred, nine hundred .

The numeral eleven is written with НН from the expression one-on-twenty , where - twenty means ten.

Simple numerals from 5 to 10 and complex numerals, which end at - (from 11 to 20 and 30 ), are written with a soft sign ( b ) at the end:

five, thirty .

When declining these numerals, only their endings change:

five - five, thirty - thirty .

Complex numbers that end at -thousand ( 50 -80 ) and at -SOT ( 500 -900 ), are written with a soft sign ( b ) in the middle:

seventy, seventy, seventy, seventy, seventy. seven hundred .

Declension changes both parts of these numbers: 90

	M. and Wed. genus	J. Rod
I., V.	One and a half	One and a half
R., D., T., P.	Fi -
osta

Soft sign in numerals

**Spelling of the soft sign in numerals**
at the end thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, thirty
in the middle	fifty, sixty, seventy, eighty, five hundred, six hundred, seven hundred, eight hundred, nine hundred

Soft sign ь is not written in the middle of the following numbers:

fifteen, sixteen, seventeen, eighteen, nineteen.

Numeral

FLOOR

Instead of the word half its abbreviated version is often used - floor . The numeral floor with other words can be written together, separately or with a hyphen.

one piece	As part of compound words, the second part of which begins with a consonant letter.	half past two half an hour half a glass
one piece	As part of adverbs.	half voice half turn half voice
hyphenated	Before vowels.	half an apple half a watermelon
	Before a consonant L .	half a lemon half a liter
	Before proper names.	half of Moscow half of Italy
separately	If gender has an independent meaning and there is an agreed definition between it and the noun.	half a coffee cup half past three in the night

Syntactic role

In sentences, cardinal numbers can be any member of the sentence. Cardinal numbers with nouns dependent on them are one member of the sentence. For example:

Ten is divisible by two.

Three kittens were playing on the lawn near the house.

After an unexpected defeat, there were nine of us left.

I took out five coins from my pocket.

Extra classes were supposed to start at five o'clock.

Cardinal numbers / Name numerals / Morphology and morphological analysis / Reference book on the Russian language for elementary school

Main
Handbooks
Primary school Russian language guide
Morphology and morphological analysis
Numeral name
Cardinal numbers

Cardinal numbers are numbers that indicate a number or quantity and answer the question how much? - five, twenty, sixty, one hundred, one hundred and forty.

Cardinal numbers in their composition are:

simple - they consist of one word containing one root - one, two, forty.
complex - they consist of one word , but in the word there are two roots and more - fifty, seventy.
compound - they consist of several words - fifty one, one hundred and forty.

Fractional numbers are a kind of compound numbers.

Cardinal numbers change by cases . Gender and number they do not have - three berries, three bananas, three apples.

Exception - one, two. The numeral one changes according to gender and number - one object, one picture, one window, one cream. The numeral two has only two generic forms: masculine and neuter - form two (two clouds, two chairs), feminine - form two (two baskets).

You can read more about the declension of cardinal numbers here - declension of numerical names.

Cardinal numbers are combined with the noun - either agree with it or govern:

if the numeral is in the nominative or accusative case, then it governs the noun , which is in genitive case - three chairs, ten fruits.
Learn more