Cardinal numbers example

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.

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 1st, 2nd, 3rd, 4th, 5th, 10th, 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.

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

1. 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.

2. 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.

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Practice Questions on Cardinal Numbers

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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 - Explanation, Solved Examples and FAQs

What Are Cardinal Numbers?

Cardinal numbers are the generalization of natural numbers as it consists of all the counting numbers starting from one. Cardinal numbers are also called cardinals. The term cardinal numbers or cardinal was coined to represent the size of a set called cardinality (size) of sets. Cardinality is the number of elements present in a finite set which usually describes the size of the sets. For example, let us take two sets - Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 5, 7}. The cardinality of set A is 4 as there are 4 elements present in set A whereas the number of elements present in set B is 5 so the cardinality of set B is 5. Cardinal tells us how many of something is present such as one, two, three, four, five, etc. 

Apart from cardinal numbers, there are two other numbers that are ordinal and nominal. Cardinal number tells us how many of something is present, ordinal number describes the position of things and nominal number usually represents the name. For example, there were 11 players playing a game where each player has a number printed on the shirt that represents him. Suppose player number 33 comes first. Then, in this case, the cardinal number is 11 because there are a total of eleven players, the ordinal number of the player who won is 1st and the nominal number is 33 as it represents the player who one. 

Summary

• Cardinal Number (How many): 11

• Ordinal Number (Position): 1st

• Nominal Number (Name): 33

How Many Cardinal Numbers are There?

Cardinal numbers are used as counting numbers. Counting can be of less number of things or more number of things. For example, we can count the number of fans in a house, the number of sheep on the farm, the number of hairs in our head, or the number of stars in the sky. All can be counted by using numbers like one, two, three, four, and so on. The counting can go on to infinity but there are a limited number of digits used. Basically there are 10 digits used to represent any number and those digits are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. Zero (0) alone is not a cardinal number. But zero can be used with other digits to represent numbers like 10, 20, 30, 700, 9000, etc.  The combination of numbers is used in series 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Once the number becomes double-digit, we change the ones of the number following the series. Example, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. Here, the digit in tens place remains constant while the digit in one place follows the series. 

Once the series in one place reaches the end (i. e, 9), the digit in ten’s place is changed to a number of higher-order and the pattern is followed. Example, 20, 21, 22, 23, 24, 25, 26 27, 28, 29. The pattern is followed until one’s reaches 99. After all the numbers in two digits are over, three-digit numbers are followed. The three-digit number starts from 100 and goes on till 999. Three-digit numbers are followed by four-digit numbers and so on. Therefore, there is no limit to the cardinal numbers. 

Solved Examples

Example 1: Show how you can coordinate cardinal numbers with ordinal numbers?

Solution: Cardinal numbers and ordinal numbers can be coordinated as shown below:

Cardinal numbers: digits, spelling.

• 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:

1. Integers (denoting an integer):

   one, twenty-five, one hundred .

2. 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:

   	M. and Wed. genus	J. Rod
   I., V.	One and a half	FILE
   R., D., T., P.	9011 9019

3. 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 numerals that end at -thousand ( 50 -80 ) and at -hundred ( 500 -900 ), are written with a soft sign ( b ) in the middle:

seventy, seventy, seventy, seventy, seven hundred .

Declension changes both parts of these numbers: 90 osta

Soft sign in numerals

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

fifteen, sixteen, seventeen, eighteen, nineteen.

Numeral

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
	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 part 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 in English

In this article we will get acquainted with English cardinal numbers, namely, whole numbers.

Cardinal numbers answer the question "how much" and indicate the exact amount.

Examples

They have two children. They have two children.

There are five oranges in the bowl. There are five oranges in a bowl.

I've had three Zoom meetings today. I had three zoom conferences today.

Numbers from 1 to 12

These numbers must be memorized.

Numbers from 13 to 19

All these numbers end in -teen , the stress falls on the same syllable.

Numbers 20 to 99

All round tens end in -ty . Here is their list.

To form a non-round two-digit number, we simply add a second digit to the tens. In this case, a hyphen is put on the letter.

Examples

21 → twenty-one

46 → forty-six

99 → ninety-nine

Numbers greater than 100

Milliard or billion?

The word billion comes from American English. Before that, the British, like us, used to say milliard. However, in the 1970s, the American version, billion, was officially adopted. Gradually, it spread and replaced the old word milliard. Today, billion is common not only in international finance, but also in colloquial speech. nine hundred and ninety-nine

Note

Omitted in American English and . For example, one hundred eighty-six, two hundred seventy-three, etc.

With larger numbers, the same principle holds. As in Russian, we voice numerals from left to right, sequentially listing millions, thousands, hundreds, tens and ones. Please note that after thousand, million, billion the union and is already not put