Cardinal Numbers and Ordinal Numbers

Cardinal numbers and ordinal numbers are explained here with the help of colorful pictures.

We count the number of objects like this:

One, two, three, four, five, six, seven, eight, nine, ten, eleven, ...

The number on which our counting ends tells us the number of objects. Suppose, we have a collection of balls.

Cardinal Numbers


We can count these balls by labelling them as shown on the left. Our counting ends at 6.

So, there are 6 balls in the collection.


The numbers 1,2,3,... which tell us the number of objects or items are called cardinal numbers.

Now suppose, 5 children are standing in a queue at the bus stop.

Ordinal Numbers

We say that:

1. James is first in the queue.

2. Olivia is second in the queue.

3. Sophia is third in the queue.

4. Daniel is fourth in the queue.

5. Nora is fifth in the queue.

The numbers such as first, second, third, fourth, fifth which tell us the position or rank of an object in an ordered collection, are called ordinal numbers.

cardinal numbers and ordinal numbers

There are many steps in a staircase as shown in the above figure. The given staircase has nine steps, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9.

In the process of climbing up the stairs, we term step Number (1) as the first step, step Number (2) as the second step number (3) as the third step, Number (4) as the fourth step, Number (5) as the fifth step, Number (6) as sixth step, Number (7) as seventh step, Number (8) as eighth step and Number (9) as ninth step. These are also expressed as 1ˢᵗ, 2ⁿᵈ, 3ʳᵈ, 4ᵗʰ, 5ᵗʰ, 6ᵗʰ, ………… etc.

Numbers 1, 2, 3, 4, 5, ……, 9, etc., are called cardinal numbers while 1ˢᵗ, 2ⁿᵈ, 3ʳᵈ, 4ᵗʰ, 5ᵗʰ, 6ᵗʰ, ………… etc., are known as ordinal numbers.

The cardinal numbers express the quantitative property of the numbers while the ordinal numbers express their order. The cardinal numbers express the number of objects in a collection while the ordinal number always expresses one object.

For example, there are five students in a row (cardinal number) and fifth student of the row (ordinal number).

While coming down the stairs the ordinal numbers are changed. The 9ᵗʰ becomes the 1ˢᵗ, the eighth becomes 2ⁿᵈ, the seventh becomes 3ʳᵈ and so on. Thus, ordinal numbers are changed in reverse order, i.e., the last becomes the first, the last but one becomes the second, etc. But the cardinal numbers remain the same.


Cardinal numbers      
showing serial number        1  2  3   4  5  6  7  8  9
of steps of staircase       


Ordinal numbers      
     from                              1st  2nd  3rd   4th  5th  6th  7th  8th  9th
   the front      


Ordinal numbers      
     from                              9th  8th  7th   6th  5th  4th  3rd  2nd  1st
   the back       


Thus, the ordinal numbers indicate the position of an object from the front or back of any given object. 

Let us imagine that, there are seven boys in a row who are numbered as 1, 2, 3, 4, 5, 6 and 7 from one end of the row. These numbers are called cardinal numbers. 

For example:

 Ordinal Numbers from 1 to 7: 1st   2nd   3rd   4th   5th  6th   7th

 Ordinal Numbers from 7 to 1: 7th   6th   5th   4th   3rd   2nd   1st

Now if we take the position of each boy from boy number (1). The position of each boy is indicated by ordinal numbers. These are from left to right as 1st,   2nd,   3rd,   4th,   5th,   6th,   7th and from right to left as 7th,   6th,   5th,   4th,   3rd,   2nd,   1st. 

Thus, from both sides the position of each boy may be indicated by ordinal numbers.


REPRESENTATION OF ORDINAL NUMBERS

In figures, the ordinal numbers are indicated by counting numbers but we suffix two letters every time. The first, second and third are shown by adding the letters 'st', 'nd' and 'rd' respectively. All the other ordinal numbers are shown by adding 'th'.


The first ten ordinal numbers are given below in words and figures:

Ordinal Numbers

Representation

First

1st

Second

2nd

Third

3rd

Fourth

4th

Fifth

5th

Sixth

6th

Seventh

7th

Eighth

8th

Ninth

9th

Tenth

10th


Ordinal numbers tell us the position number of objects.

Ordinal Numbers


The Meaning of Ordinals:

The drill teacher asked some 5 boys to stand in a line. The 5 boys stood in a line in the following order :- Peter, Ramesh, John, Ahmed and David.

Here Peter is the first boy in the line.

Ramesh is the second boy in the line.

John is the third boy in the line.

Ahmed is the fourth boy in the line.

David is the fifth boy in the line.


Peter is the first boy and David is the last boy. In between, there are Ramesh, John and Ahmed. When we talk of Ramesh, we say he is the second boy in the line, and when we talk of John, we say he is the third boy in the line and so on.

Here first, second, third, fourth and fifth are ordinal numbers, corres- ponding to 1, 2, 3, 4, 5. We write

first as 1st,

second as 2nd,

third as 3rd

fourth as 4th,

fifth as 5th,

sixth as 6th.


Who stood first in the Arithmetic Test?

Rama stood third in the English Test.

David was second in the Drawing Test.

What is the meaning of first, second and third here?

First, second, third are the ordinal numbers.

Ordinal and Cardinal Numbers


Questions and Answers on Cardinal Numbers and Ordinal Numbers:

1. From the left, tick (✔) fifth fruit:

Fifth - Ordinal Numbers

Answer:

1.

Fifth - Ordinal Numbers Answer


2. From the right, cross () the third bird:

Third - Ordinal Numbers

Answer:

2.

Third - Ordinal Numbers Answer


3. Look at the flowers arranged in a row and write the position of purple flower from the left:

Position - Ordinal Numbers

Answer:

3. sixth


4. Match the correct ordinal number from the column-1 with the expression in the column-2:

Column-1

                     Column-2

Sixth

The __________ of April is a Fool's Day.

Third

J is the __________ letter of English alphabet.

Tenth

July is the __________ month of the year.

First

C is the __________ letter of English alphabet.

Seventh

Friday is the __________ day of the week.


Answer:

4. The first of April is a Fool's Day.

J is the tenth letter of English alphabet.

July is the seventh month of the year.

C is the third letter of English alphabet.

Friday is the sixth day of the week.


5. Write the order of each letter in the word, MANGO:

(i) A is the __________ letter of the given word.

(ii) M is the __________ letter of the given word.

(iii) O is the __________ letter of the given word.

(iv) N is the __________ letter of the given word.

(v) G is the __________ letter of the given word.


Answer:

5. (i) second

(ii) first

(iii) fifth

(iv) third

(v) fourth


6. Fill in the boxes to write the names of these great cricket players:

(i)

The 2nd letter is A.

The 5th letter is I.

The 3rd letter is C.

The 1st letter is S.

The 4th letter is H.

The 6th letter is N.



▢▢▢▢▢▢



(ii)

The 3rd letter is P.

The 5th letter is L.

The 2nd letter is A.

The 4th letter is I.

The 1st letter is K.


▢▢▢▢▢


Answer:

6. (i) SACHIN

(ii) KAPIL


7. Colour the second ball red, fifth ball blue and seventh ball green.

Cardinal Numbers and Ordinal Numbers


Answer:

7. 

Cardinal Numbers and Ordinal Numbers Answer


8. Colour the 7th ball orange, 3rd ball purple and 8th ball brown.

Cardinal Numbers and Ordinal Numbers


Answer:

8. 

Cardinal Numbers and Ordinal Numbers


9. Fill in the boxes to find the name of this great man.

The 8th letter is I.

The 2nd letter is A.

The 1st letter is G.

The 4th letter is D.

The 5th letter is H.

The 7th letter is J.

The 3rd letter is N.

The 6th letter is also I.

Cardinal Numbers - Great Man
Cardinal and Ordinal Numbers


Answer:

9.

Cardinal and Ordinal Numbers Answer


10. Write the position. One has been done for you.

(i)

The position of H in

ELEPHANT

is

   fifth   

(ii)

The position of A in

PEACOCK

is

              

(iii)

The position of Y in

MONKEY

is

              

(iv)

The position of E in

TIGER

is

              

Answer:

10. (ii) third

(iii) sixth

(iv) fourth

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