Cardinal Numbers | Cardinal Numbers vs. Ordinal Numbers

Last Updated on November 8, 2023

Cardinal numbers are an essential part of our everyday lives, even if we don’t realize it. From counting the number of apples in a basket to measuring the distance between two cities, cardinal numbers play a crucial role in our daily activities. These numbers are the foundation of mathematics and form the basis for many other mathematical concepts, such as addition, subtraction, multiplication, and division. This article will provide you with a comprehensive understanding of the importance of cardinal numbers.

Cardinal Numbers

Cardinal NumbersPin

What Are Cardinal Numbers?

Cardinal numbers are numbers that are only used for counting and are usually called counting numbers. Cardinals are the numbers that are used to determine how many of something there is or the quantity. If you want to know how many of something there is then you have to count them, and that is where the cardinal numbers come in.

The lowest cardinal number is one. Zero is not a cardinal number as to count how many of something you have, you have to have something in the first place, but every number up from there is a cardinal. However, fractions and decimals are not cardinal numbers as they are not whole numbers, they only represent a part of a group or set.

Examples of Cardinal Numbers

Cardinal numbers are numbers that are on their own, digits such as one (1), two (2), three (3), four (4), five (5), six (6), seven (7) and so on.

For example:

  • Frank has five pens.

The cardinal number here is five as that is how many pens he has.

  • Laura came second in the spelling test as she got nine questions right.

Here the cardinal number is nine as that is the number that is telling us how many questions she got right.

  • Helen has two dogs and three cats.

Both two and three are cardinal numbers in this sentence as they are telling us how many cats and dogs she has.

  • Jack has one dog and two cats, but he has seven pets in total as he has some goldfish as well.

One, two and seven are all cardinal numbers here as they are all telling us how many of something Jack has.

Cardinal Numbers vs. Ordinal Numbers

As well as using cardinal numbers in our everyday life we also use ordinal numbers all the time. Ordinal numbers are the numbers such as first (1st), second (2nd), third (3rd), fourth (4th), fifth (5th), sixth (6th), seventh (7th) and so on. While cardinal numbers are the ones that tell us how many of something there is, ordinal numbers are the numbers that tell us the position of something rather than the quantity.

For example:

  • Laura came second in the spelling test as she got nine questions right.

Here the ordinal number is two as that is the number that is telling us which position Laura came in the spelling test, while we have already established that nine is the cardinal number in this sentence.

  • There were twenty people in the race and she finished third.

The cardinal number is twenty (how many) and the ordinal number is three (position).

  • There were twenty five people in the race. Lisa finished first and Tom finished fourth.

The cardinal number in this sentence is twenty five, while the ordinal numbers are one and three as they are both telling us the position.

  • Jill isn’t very good at running – she only managed to pass two people. Her sister, Jane, won the race though.

Here the cardinal number is two as that is the number of people that Jill passed, while the ordinal number is one as Jane finished first in the race.

Frequently Asked Questions

What is the meaning of cardinal numbers in mathematics?

Cardinal numbers are the numbers used for counting real objects or things. In mathematics, they represent the size of a set and help us answer the question “How many?”. Examples of cardinal numbers include 1, 2, 3, 4, 5, and so on.

How do you find the cardinal number of a set?

To find the cardinal number of a set, simply count the number of elements in the set. For example, if we have a set {A, B, C, D}, the cardinal number of this set would be 4, as there are four distinct elements present in the set.

What is the difference between cardinal and ordinal numbers?

Cardinal numbers represent the quantity or size of a set, whereas ordinal numbers indicate the position or order of elements within a set. For example, “first,” “second,” and “third” are ordinal numbers, while 1, 2, and 3 are cardinal numbers.

What are some examples of cardinal numbers in French?

In French, cardinal numbers are similar to those in English. Here are a few examples:

  • un (1)
  • deux (2)
  • trois (3)
  • quatre (4)
  • cinq (5)

Can you give examples of ordinal and cardinal numbers?

Certainly! Here are some examples of ordinal and cardinal numbers:

Ordinal numbers:

  • first (1st)
  • second (2nd)
  • third (3rd)

Cardinal numbers:

  • one (1)
  • two (2)
  • three (3)

How does the cardinal number concept differ from whole numbers?

Cardinal numbers and whole numbers are closely related. All cardinal numbers are whole numbers, but not all whole numbers are cardinal numbers. Cardinal numbers specifically refer to counting numbers (1, 2, 3, etc.), while whole numbers also include zero (0) and sometimes negative integers like -1, -2, -3, and so on. 

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