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The worksheet on Cardinal Numbers and Ordinal Numbers is here. Get the various examples of cardinal and ordinal numbers exercises for grade 2. All the students can easily know the tips to solve these kinds of problems. Know the definitions of cardinals and ordinals in the next section. Ordinal Numbers are defined as numbers that tell us the position of that number. Cardinal Numbers are defined as the quantity. These numbers are used for counting.

Read More:

• Worksheet on Ordinals
• Cardinal Number of a Set

Worksheet on Cardinal Numbers and Ordinal Numbers

Problem 1:

Different colour and shaped vegetables are placed in the line as shown in the picture.
The first one is carrot.
(i) How many vegetables are present in total?
(ii) How many vegetables are in red colour?
(iii) Which vegetable is in the sixth position?
(iv) Which vegetable is in the ninth position?
(v) Ginger is placed in which position?
(vi) Peas is placed in which position?

Solution:

To find the ordinal and cardinal values, we mention it in a table.

Cardinal Number	Ordinal Numbers		Vegetable (from Left to Right)
1	1st	first	Carrot
2	2nd	second	Brinjal
3	3rd	third	Tomato
4	4th	fourth	Cauliflower
5	5th	fifth	Onion
6	6th	sixth	Peas
7	7th	seventh	Turnip
8	8th	eighth	Potato
9	9th	ninety	Lemon
10	10th	tenth	Ginger

As given in the question,
(i) There are 10 vegetables in total
(ii) There are 2 vegetables in red colour
(iii) Peas is in the sixth position
(iv) Lemon is in the ninth position
(v) Ginger is placed in 10th position
(vi) Peas is placed in the sixth position

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Problem 2: 
Different colour and shaped fruits are placed in the line as shown in the picture.
The first one is a banana.
(i) How many fruits are present in total?
(ii) How many fruits are in red colour?
(iii) Which fruit is in the sixth position?
(iv) Which fruit is in the third position?
(v) Watermelon is placed in which position?
(vi) Apple is placed in which position?

Solution:

To find the ordinal and cardinal values, we mention them in a table.

Cardinal Number	Ordinal Numbers		Vegetable (from Left to Right)
1	1st	first	Banana
2	2nd	second	Watermelon
3	3rd	third	Grapes
4	4th	fourth	Strawberry
5	5th	fifth	Pear
6	6th	sixth	Orange
7	7th	seventh	Apple
8	8th	eighth	Green Apple

As given in the question,
(i) There are 8 fruits in total
(ii) There are 3 fruits in red colour
(iii) Orange fruit is in the sixth position
(iv) Grapes are in the third position
(v) Watermelon is placed in the second position
(vi) Apple is placed in the seventh position

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Problem 3:
Write the cardinal numbers in words for the following numbers – 4th, 7th, 13th, 22nd, 28th, 33rd, 11th, 50th, 38th, 2nd?

Solution:

As given in the question,
The numbers are 4th, 7th, 13th, 22nd, 28th, 33rd, 11th, 50th, 38th, 2nd

Cardinal Numbers	Ordinals
1	4th	Fourth
2	7th	Seventh
3	13th	Thirteenth
4	22nd	Twenty-Second
5	28th	Twenty-Eighth
6	33rd	Thirty-Three
7	11th	Eleventh
8	50th	Fiftieth
9	38th	Thirty-Eighth
10	2nd	Second

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Problem 4: 

Eleventh	Four	Eight	Thirteenth	Seventeenth
Thirtieth	Twelveth	Twenty-Third	Three	One
Twenty-First	Nine	Seventy-Three	Sixtieth	Forty-fifth
Thirty	Third	Three	Twenty-fifth	Sixty-one

In the above table, the ordinal numbers are represented with blue colour and cardinals are represented with green colour. Find the ordinal and cardinal numbers?

Solution:

As given in the question,
The ordinal numbers are expressed with blue colour and cardinal numbers are expressed with green colour.
Therefore, the ordinal numbers are
Eleventh – 11th
Thirteenth – 13th
Seventeenth – 17th
Thirtieth – 30th
Twelveth – 12th
Twenty-First – 21st
Sixtieth – 60th
Forty-Fifth – 45th
Third – 3rd
Twenty-fifth – 25th
The cardinal numbers are
Four – 4
Eight – 8
Three – 3
One – 1
Nine – 9
Seventy-Three – 73
Thirty – 30
Three – 3
Sixty-one – 61

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Problem 5:

Here, there is a list of students and their scores in the Quiz:

S. No	Name	Quiz Marks
1	Anju	12
2	Anurag	15
3	Dheeraj	10
4	David	6
5	Fatima	9
6	Farheen	8
7	Julie	6
8	John	10
9	Kale	6
10	Samuel	8

Find the ordinal and cardinal numbers of the following questions:
(i) Who scored the highest marks in the quiz?
(ii) Who scored the second-highest marks in the quiz?
(iii) How many of them scored 6 marks on the quiz?
(iv) What position did Dheeraj get in the quiz?
(v) What position did Farheen get in the quiz?

Solution:

As given in the question,
The list of students scoring marks in the quiz are given
(i) To find the student who scored position 1, we have to find the student with the highest score
Therefore, the student who scored position 1 is Anurag
The ordinal value of the student Anurag is first
The cardinal value of the student Anurag is 1
(ii) To find the student who scored position 2, we have to find the student with the second-highest score
Therefore, the student who scored position 2 is Anju
The ordinal value of the student Anju is second
The cardinal value of the student Anju is 2
(iii) To find the students who scored 6 marks, we check for no of 6 in the marks column
Therefore, the students who scored 6 marks are 3
The ordinal value of the students who scored 6 marks is third
The cardinal value of the students who scored 6 marks is 3
(iv) Dheeraj got the third position in the quiz
The ordinal value of the student Dheeraj is third
The cardinal value of the student Dheeraj is 3
(v) John got the fifth position in the quiz
The ordinal value of the student John is fifth
The cardinal value of the student John is 5

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Problem 6:

Names	Marks
Alex	22
Racheal	25
Ross	36
Monica	32
Chandler	16
Phoebe	17
Joey	24

Here is the list of marks scored by various students in the Maths Exam, then
Find the ordinal and cardinal numbers of the following questions:
(i) Who scored the highest marks in maths?
(ii) Who scored the second-highest marks in maths?
(iii) How many of them scored 36 marks on the quiz?
(iv) What position did Pheobe get in the quiz?
(v) What position did Racheal get in the quiz?

Solution:

As given in the question,
The list of students scoring marks in maths are given
(i) To find the student who scored position 1, we have to find the student with the highest score
Therefore, the student who scored position 1 is Ross
The ordinal value of the student Ross is first
The cardinal value of the student Ross is 1
(ii) To find the student who scored position 2, we have to find the student with the second-highest score
Therefore, the student who scored position 2 is Monica
The ordinal value of the student Monica is second
The cardinal value of the student Monica is 2
(iii) To find the students who scored 36 marks, we check for no of 36 in the marks column
Therefore, the students who scored 36 marks is only 1
The ordinal value of the students who scored 36 marks is oneth
The cardinal value of the students who scored 36 marks is 1
(iv) Pheobe got the sixth position in the quiz
The ordinal value of the student Pheobe is sixth
The cardinal value of the student Pheobe is 6
(v) Racheal got the third position in the quiz
The ordinal value of the student Racheal is third
The cardinal value of the student Racheal is 3

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Problem 7:

Here is the list of fruits in the line as shown in the picture. Consider that Apple is 1st fruit, then
(i) Which fruit is in the third place?
(ii) Which fruit is in the fifth place?
(iii) Find the place of the cherry fruit?
(iv) Find the place of the peach fruit?

Solution:

As given in the question,
From the list of fruits,
The first fruit is the apple
The second fruit is the pear
The third fruit is the cherry
The fourth fruit is the peach
The fifth fruit is watermelon
(i) The fruit that is in the third place is cherry
The ordinal number of the cherry fruit is third
The cardinal number of the cherry fruit is 3
(ii) The fruit that is in the fifth place is watermelon
The ordinal number of the watermelon is fifth
The cardinal number of the watermelon is 5
(iii) The place of the cherry fruit is third
The ordinal number of the cherry fruit is third
The cardinal number of the cherry fruit is 3
(iv) The place of the peach fruit is fourth
The ordinal number of the peach fruit is fourth
The cardinal number of the peach fruit is 4

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Problem 8:
Write the ordinal and cardinal numbers for the following: 13th, 19th, 27th, 28th, 30th, 32nd, 34th?

Solution:

As given in the question,
The numbers are 13th, 19th, 27th, 28th, 30th, 32nd, 34th
The ordinal numbers are
13th – Thirteenth
19th – Nineteenth
27th – Twenty-Seventh
28th – Twenty-Eighth
30th – Thirtieth
32nd – Thirty-Second
34th – Thirty-Fourth
The cardinal numbers are
13th – 13
19th – 19
27th – 27
28th – 28
30th – 30
32nd – 32
34th – 34

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Problem 9:

Here is the calendar of the month of January, then find
(i) Find the ordinal numbers of Mondays?
(ii) Indicate the cardinal numbers of each Tuesday?
(iii) Find the date of the first Sunday(Note its ordinal and cardinal number)
(iv) Find the date of the last Friday of the month?
(v) Find all the dates on Thursday?

Solution:

As given in the question,
From the January calendar,
(i) The ordinal numbers of Monday are sixth, thirteenth, twentieth, twenty-seventh
(ii) The cardinal numbers of Tuesday are 7, 14, 21 and 28
(iii) The date of the first Sunday is 5
The ordinal number of the first Sunday is fifth
The cardinal number of the first Sunday is 5
(iv) The date of the last Friday of the month is 31st
The ordinal number of last Friday is Thirty-First
The cardinal number of last Friday is 31
(v) All the dates of Thursday are 2nd, 9th, 16th, 23rd, 30th
The ordinal numbers are second, ninth, sixteenth, twenty-third, thirtieth
The cardinal numbers are 2, 9, 16, 23, 30

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Problem 10:

Names	Marks
Alen	12
Randy	5
Rose	11
Mon	14
Chand	8
Philip	8
John	4

Here is the list of marks scored by various students in the English Exam, then
Find the ordinal and cardinal numbers of the following questions:
(i) Who scored the highest marks in English?
(ii) Who scored the second-highest marks in English?
(iii) How many of them scored 8 marks on the quiz?
(iv) What position did Chand get in the quiz?
(v) What position did Rose get in the quiz?

Solution:

As given in the question,
The list of students scoring marks in English are given
(i) To find the student who scored position 1, we have to find the student with the highest score
Therefore, the student who scored position 1 is Mon
The ordinal value of the student Mon is first
The cardinal value of the student Mon is 1
(ii) To find the student who scored position 2, we have to find the student with the second-highest score
Therefore, the student who scored position 2 is Alen
The ordinal value of the student Alen is second
The cardinal value of the student Alen is 2
(iii) To find the students who scored 8 marks, we check for no of 8 in the marks column
Therefore, the students who scored 36 marks is 2
The ordinal value of the students who scored 36 marks is two
The cardinal value of the students who scored 36 marks is 2
(iv) Chand got the fourth position in the quiz
The ordinal value of the student Chand is fourth
The cardinal value of the student Chand is 4
(v) Rose got the third position in the quiz
The ordinal value of the student Rose is third
The cardinal value of the student Rose is 3

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Ordinal numbers are generally used to mention the position of each item when a number of items are present. You can check the worksheet on ordinals along with the solutions. Know how to denote the ordinal numbers for a set of numbers. Answer all the questions with the given ordinal and cardinal numbers. Go through the below sections to know the example problems on numbers and their names along with the solution.

The list of the first 30 ordinal numbers are:

Ordinal Numbers Worksheet with Answers

Problem 1: 

Consider that Apple is 1st fruit, then
(i) Which fruit is the third one?
(ii) Which fruit is the fifth one?
(iii) Which place is the cherry fruit in?
(iv) Which place is the peach in?

Solution:

As given in the question,
Apple is the first fruit
Pear is the second fruit
Cherry is the third fruit
Peach is the fourth fruit
Watermelon is the fifth fruit
From the question,
(i) The third fruit is cherry fruit
(ii) The fifth fruit is watermelon
(iii) Cherry fruit is in third place
(iv) Peach is in second place

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Problem 2:
Write the ordinal numbers in words for the following: 11th, 15th, 17th, 18th, 20th, 22nd, 24th?

Solution:

As given in the question,
The ordinal numbers are 11th, 15th, 17th, 18th, 20th, 22nd, 24th
The numbers in words are
11th – Eleventh
15th – Fifteenth
17th – Seventeenth
18th – Eighteenth
20th – Twentieth
22nd – Twenty-second
24th – Twenty-forth

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Problem 3:
Here, there is a list of students and their scores in the Quiz:

S. No	Name	Quiz Marks
1	Anjali	6
2	Antony	8
3	Duke	12
4	Dunkin	10
5	Emily	7
6	Ester	8
7	Eric	7
8	Jessy	11
9	Kaur	9
10	Sam	8

(i) Who scored position 1?
(ii) Who scored position 2?
(iii) Who scored position 3?
(iv) Who scored position 4?

Solution:

As given in the question,
The list of students scoring marks in the quiz are given
(i) To find the student who scored position 1, we have to find the student with the highest score
Therefore, the student who scored position 1 is Duke
(ii) To find the student who scored position 2, we have to find the student with the second-highest score
Therefore, the student who scored position 2 is Jessy
(iii) To find the student who scored position 3, we have to find the student with the third-highest score
Therefore, the student who scored position 3 is Dunkin
(iv) To find the student who scored position 4, we have to find the student with the fourth-highest score
Therefore, the student who scored position 4 is Kaur

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Problem 4: 
Answer the ordinals numbers associated with alphabets?
(i) A is the ___ letter of the alphabet
(ii) C is the ___ letter of the alphabet
(iii) F is the ___ letter of the alphabet
(iv) G is the ___ letter of the alphabet

Solution:

As given in the question,
We have to find the ordinal numbers associated with the alphabets
(i) A is the first letter of the alphabet
(ii) C is the third letter of the alphabet
(iii) F is the sixth letter of the alphabet
(iv) G is the seventh letter of the alphabet
Therefore, the ordinal numbers here are first, third, sixth and seventh

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Problem 5: 
Colour the balls which are given above:
Colour the first(1st) ball red
Colour the second(2nd) ball blue
Color the third(3rd) ball green
Colour the fourth(4th) ball yellow
Colour the fifth(5th) ball pink
Colour the sixth(6th) ball purple
Colour the seventh(7th) ball orange
Colour the eighth(8th) ball grey

Solution:

As given in the question,
We have to colour all the balls with different colours, then we get the final solution as

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Problem 6:

Different popsicles are coloured with different colours, then
(i) Find the colour of the fourth popsicle?
(ii) Find the colour of the first popsicle?
(iii) Find the position of the green popsicle?
(iv) Find the position of the red popsicle?

Solution:

As given in the question,
There are 5 popsicles with different colours
(i) The colour of the fourth popsicle is Orange
(ii) The colour of the first popsicle is Purple
(iii) The position of the green popsicle is third(3rd)
(iv) The position of the red popsicle is fifth(5th)

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Problem 7:

Different colour cars are parking in a parking lot, then
(i) Find the colour of the first car
(ii) Find the colour of the second car
(iii) Find the position of the yellow car
(iv) Find the position of the blue car

Solution:

As given in the question,
Different colour cars are parking in a parking lot
(i) The colour of the first car is green
(ii) The colour of the second car is red
(iii) The position of the yellow car is third
(iv) The position of the blue car is fifth

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Problem 8: 
Write the ordinal numbers in words for the following: 9th, 11th, 12th, 16th, 26th, 30th, 34th?

Solution:

As given in the question,
The ordinal numbers are 9th, 11th, 12th, 16th, 26th, 30th, 34th
The numbers in words are
19th – NIneth
11th – Eleventh
12th – Twelveth
16th – Sixteenth
26th – Twenty-Sixth
30th – Thirtieth
24th – Twenty-forth

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Problem 9:
Different colours teddy bears are here, then
(i) Find the colour of the fourth teddy bear
(ii) Find the colour of the second teddy bear
(iii) Find the position of the blue teddy bear
(iv) Find the position of the green teddy bear

Solution:

As given in the question,
The different colours of teddy bears are here
(i) The colour of the fourth teddy bear is red
(ii) The colour of the second teddy bear is pink
(iii) The position of the blue teddy bear is fifth
(iv) The position of the green teddy bear is third

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Problem 10:

Different colours snails are here, then
(i) Find the colour of the fourth snail
(ii) Find the colour of the second snail
(iii) Find the position of the red snail
(iv) Find the position of the violet snail

Solution:

As given in the question,
The different colours of snails are here
(i) The colour of the fourth snail is brown
(ii) The colour of the second snail is green
(iii) The position of the red snail is three
(iv) The position of the violet snail is first

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Worksheet on Place Value and Face Value is given here. Solve various questions of place value and face values. Know the difference between them and also the steps to solve the problems. Identify the digits place of the number and determine its place value. Check various questions involved in face value and place value along with the solutions in the further modules.

Place value is determined as the position of the digit in the number and face value is defined as the actual value of the digit in the number.

Read More Articles:

Place Value in Words and Numbers	Worksheet on Tens and Ones	Problems related to Place Value
International Place Value Chart	Face Value and Place Value	Finding and Writing the Place Value
Thousandths Place in Decimals	Place Value	Place Value Chart

Worksheet on Place Value and Face Value

Problem 1:
Write the place value and face value of 782?

Solution:

As given in the question,
The number is 782
To find the place value, we have to know the position of digits,
i.e., The digit 2 is at one place
The digit 8 is at tens place
The digit 7 is at hundreds place
Therefore, the place values are
The place value of 2 is 2
The place value of 8 is 80
The place value of 7 is 700
To find the face value, we have to know the value of the digit
The face value of 2 is 2
The face value of 8 is 8
The face value of 7 is 7

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Problem 2:
Write the place value and face value of 267?

Solution:

As given in the question,
The number is 267
To find the place value, we have to know the position of digits,
i.e., The digit 7 is at ones place
The digit 6 is at tens place
The digit 2 is at hundreds place
Therefore, the place values are
The place value of 7 is 7
The place value of 6 is 60
The place value of 2 is 200
To find the face value, we have to know the value of the digit
The face value of 7 is 7
The face value of 6 is 6
The face value of 2 is 2

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Problem 3:
Write the place value and face value of 368?

Solution:

As given in the question,
The number is 368
To find the place value, we have to know the position of digits,
i.e., The digit 8 is at ones place
The digit 6 is at tens place
The digit 3 is at hundreds place
Therefore, the place values are
The place value of 8 is 8
The place value of 6 is 60
The place value of 3 is 300
To find the face value, we have to know the value of the digit
The face value of 3 is 3
The face value of 6 is 6
The face value of 8 is 8

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Problem 4:
Write the place value and face value of 518?

Solution:

As given in the question,
The number is 518
To find the place value, we have to know the position of digits,
i.e., The digit 8 is at ones place
The digit 1 is at tens place
The digit 5 is at hundreds place
Therefore, the place values are
The place value of 8 is 8
The place value of 1 is 10
The place value of 5 is 500
To find the face value, we have to know the value of the digit
The face value of 8 is 8
The face value of 1 is 1
The face value of 5 is 5

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Problem 5:
Write the place value and face value of 970?

Solution:

As given in the question,
The number is 970
To find the place value, we have to know the position of digits,
i.e., The digit 0 is at ones place
The digit 7 is at tens place
The digit 9 is at hundreds place
Therefore, the place values are
The place value of 0 is 0
The place value of 7 is 70
The place value of 9 is 900
To find the face value, we have to know the value of the digit
The face value of 0 is 0
The face value of 7 is 7
The face value of 9 is 9

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Problem 6: 
Write > or < correctly in the blank space. 811 ___ 292, 445 ___ 682, 245 ___ 68, 282 ___ 712?

Solution:

As given in the question,
The equation is 811 ___ 292
To put the symbol correctly, first, we have to find the greater number among the two.
From the numbers, 811 and 292, the highest number is 811
Therefore, the equation will be 811 > 292
The second equation is 445 ___ 682
To put the symbol correctly, first, we have to find the greater number among the two.
From the numbers, 445 and 682, the highest number is 682
Therefore, the equation will be 445 < 682
The third equation is 245 ___ 68
To put the symbol correctly, first, we have to find the greater number among the two.
From the numbers, 245 and 68, the highest number is 245
Therefore, the equation will be 245 > 68
The fourth equation is 282 ___ 712
To put the symbol correctly, first, we have to find the greater number among the two.
From the numbers, 282 and 712, the highest number is 712
Therefore, the equation will be 282 < 712

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Problem 7:
Write the place value and face value of 5813?

Solution:

As given in the question,
The number is 5813
To find the place value, we have to know the position of digits,
i.e., The digit 3 is at ones place
The digit 1 is at tens place
The digit 8 is at hundreds place
The digit 5 is at thousands place
Therefore, the place values are
The place value of 3 is 3
The place value of 1 is 10
The place value of 8 is 800
The place value of 5 is 5000
To find the face value, we have to know the value of the digit
The face value of 3 is 3
The face value of 1 is 1
The face value of 8 is 8
The face value of 5 is 5

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Problem 8:
Write the place value and face value of 26735?

Solution:

As given in the question,
The number is 26735
To find the place value, we have to know the position of digits,
i.e., The digit 5 is at ones place
The digit 3 is at tens place
The digit 7 is at hundreds place
The digit 6 is at thousands place
The digits 2 is at ten thousand place
Therefore, the place values are
The place value of 5 is 5
The place value of 3 is 30
The place value of 7 is 700
The place value of 6 is 6000
The place value of 2 is 20000
To find the face value, we have to know the value of the digit
The face value of 5 is 5
The face value of 3 is 3
The face value of 7 is 7
The face value of 6 is 6
The face value of 2 is 2

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Problem 9:
Write the place value and face value of 843?

Solution:

As given in the question,
The number is 843
To find the place value, we have to know the position of digits,
i.e., The digit 3 is at ones place
The digit 4 is at tens place
The digit 8 is at hundreds place
Therefore, the place values are
The place value of 3 is 3
The place value of 4 is 40
The place value of 8 is 800
To find the face value, we have to know the value of the digit
The face value of 3 is 3
The face value of 4 is 4
The face value of 8 is 8

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Problem 10:
Write the place value and face value of 1978?

Solution:

As given in the question,
The number is 1978
To find the place value, we have to know the position of digits,
i.e., The digit 8 is at ones place
The digit 7 is at tens place
The digit 9 is at hundreds place
The digit 1 is at thousands place
Therefore, the place values are
The place value of 8 is 8
The place value of 7 is 70
The place value of 9 is 900
The place value of 1 is 1000
To find the face value, we have to know the value of the digit
The face value of 8 is 8
The face value of 7 is 7
The face value of 9 is 9
The face value of 1 is 1

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Worksheet on Odd and Even Numbers and solutions are here. Check how to find the odd and even numbers in the missing patterns. Find the examples with solutions in the next sections. You can get the practice material on even and odd numbers for all Grade 2 Students. Know the tips to find the missing numbers of the series. Even numbers are the integers that are exactly divisible by 2 and odd numbers are those that are not divisible by 2.

Do Refer:

• Odd and Even Numbers
• Even and Odd Numbers Between 1 and 100
• Odd Man Out

Free Worksheets on Odd and Even Numbers

Problem 1:
Find out whether the numbers are odd or even – 1, 2, 32, 35, 63, 68?

Solution:

As given in the question,
The numbers are 1, 2, 32, 35, 63, 68
Odd numbers are represented with the cross symbol and even numbers are represented with a round symbol from the above numbers.

Therefore, 1, 35, and 63 are odd numbers. 2, 32, and 68 are even numbers.

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Problem 2: 
Find out the odd and even numbers between 1 to 100?

Solution:

As given in the question,
The numbers are 1 to 100
Odd numbers are represented with the cross symbol and even numbers are represented with a round symbol from the above numbers.

Therefore, the odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99.
Therefore, the even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60,62, 64, 66, 68, 70,72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100.

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Problem 3: 
Write the odd and even numbers between 56 and 78?

Solution:

As given in the question,
The numbers are between 56 and 78
First, we will find the series of the numbers from 56 to 78
i.e., 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78
From the series above, we find the even numbers as numbers that are divisible by 2.
Therefore, the even numbers are 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78
The odd numbers are 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77

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Problem 4:
Write the odd numbers between 50 and 100?

Solution:

As given in the question,
The numbers are between 50 and 100
First, we have to find the series of the numbers from 50 and 100
i.e., 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 and 100
From the series above, we find the odd numbers which are not divisible by 2.
Therefore, the odd numbers are 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

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Problem 5:
Write the odd and even numbers between 34 and 82?

Solution:

As given in the question,
The numbers are between 34 and 82
First, we have to find the series of the numbers from 34 and 82
i.e., 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82
From the series above, we find the even numbers as numbers that are divisible by 2.
Therefore, the even numbers are 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82
The odd numbers are 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81

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Problem 6:
Write the odd and even numbers between 20 and 60?

Solution:

As given in the question,
The numbers are between 20 and 60
First, we have to find the series of the numbers from 20 and 60
i.e., 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60
From the series above, we find the even numbers as numbers that are divisible by 2.
Therefore, the even numbers are 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60
The odd numbers are 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59

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Problem 7:
Write the odd and even numbers between 29 and 91?

Solution:

As given in the question,
The numbers are between 29 and 91
First, we have to find the series of the numbers from 29 and 91
i.e., 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91
From the series above, we find the even numbers as numbers that are divisible by 2.
Therefore, the even numbers are 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90
The odd numbers are 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91

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Problem 8:
Write the odd and even numbers between 10 and 61?

Solution:

As given in the question,
The numbers are between 10 and 61
First, we have to find the series of the numbers from 10 and 61
i.e., 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61
From the series above, we find the even numbers as numbers that are divisible by 2.
Therefore, the even numbers are 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60
The odd numbers are 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59

---

Problem 9:
Write the odd and even numbers between 1 and 51?

Solution:

As given in the question,
The numbers are between 1 and 51
First, we have to find the series of the numbers from 1 and 51
i.e., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51
From the series above, we find the even numbers as numbers that are divisible by 2.
Therefore, the even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50
The odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49

---

Problem 10:
Write the odd and even numbers between 73 and 105?

Solution:

As given in the question,
The numbers are between 73 and 105
First, we have to find the series of the numbers from 73 and 105
i.e., 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105
From the series above, we find the even numbers as numbers that are divisible by 2.
Therefore the even numbers are 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104
The odd numbers are 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105

---

Problem 11:
Define whether 45, 63, 72, 84, 91 are even or odd numbers?

Solution:

As given in the question,
The numbers are 45, 63, 72, 84, 91
To define the numbers if they are odd or even, we have to check whether the numbers are divisible by 2
Check if 45 is divisible by 2, 45 is not divisible by 2 and it results in the remainder of 1
Therefore, 45 is an odd number
Check if 63 is divisible by 2, 63 is not divisible by 2 and it results in the remainder of 1
Therefore, 63 is an odd number
Check if 72 is divisible by 2, 72 is divisible by 2 and it results in the remainder of 0
Therefore, 72 is an even number
Check if 84 is divisible by 2, 84 is divisible by 2 and it results in the remainder of 0
Therefore, 84 is an even number
Check if 91 is divisible by 2, 91 is not divisible by 2 and it results in the remainder of 1
Therefore, 91 is an odd number

---

Problem 12:
Define whether 2, 5, 18, 27, 36, 48 are even or odd numbers?

Solution:

As given in the question,
The numbers are 2, 5, 18, 27, 36, 48
To define the numbers if they are odd or even, we have to check whether the numbers are divisible by 2
Check if 2 is divisible by 2, 2 is divisible by 2 and it results in the remainder of 0
Therefore, 2 is an even number
Check if 5 is divisible by 2, 5 is not divisible by 2 and it results in the remainder of 1
Therefore, 5 is an odd number
Check if 18 is divisible by 2, 18 is divisible by 2 and it results in the remainder of 0
Therefore, 18 is an even number
Check if 27 is divisible by 2, 27 is not divisible by 2 and it results in the remainder of 1
Therefore, 27 is an odd number
Check if 36 is divisible by 2, 36 is divisible by 2 and it results in the remainder of 0
Therefore, 36 is an even number
Check if 48 is divisible by 2, 48 is divisible by 2 and it results in the remainder of 0
Therefore, 48 is an even number

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If you are looking for a worksheet on numbers in expanded form, You have reached the correct page. You can also use these extra questions like expanded form with integers. Follow the detailed steps of writing numbers in expanded form worksheets for grade 2. Follow the below sections to know the models and questions of the expanded forms.

Do Refer:

• Expressing Numbers in the Expanded Form
• Expanded Form Of Decimal Fractions
• Expanded Form and Short Form of a Number

Expanded Form Worksheets with Answers

Problem 1: 
Write 14,897 in the expanded form?

Solution:

As given in the question,
The number is 14,897
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
7 – ones
9 – tens
8 – hundreds
4 – thousands
1 – ten thousand
We write the numbers as
7 – 7 * 1
9 – 9 * 10
8 – 8 * 100
4 – 4 * 1000
1 – 1 * 10000
The expansion of the number is
(7 * 1) + (9* 10) + (8 * 100) + (4 * 1000) + (1 * 10000)
7 + 90 + 800 + 4000 + 10000
Therefore, the expanded form of the number is 14, 897 is 7 + 90 + 800 + 4000 + 10000

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Problem 2: 
Write the number 9,7452 in the expanded form?

Solution:

As given in the question,
The number is 9,7452
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
2 – ones
5 – tens
4 – hundreds
7 – thousands
9 – ten thousand
We write the numbers as
2 – 2 * 1
5 – 5 * 10
4 – 4 * 100
7 – 7 * 1000
9 – 9 * 10000
The expansion of the number is
(2* 1) + (5 * 10) + (4 * 100) + (7 * 1000) + (9 * 10000)
2 + 50 + 400 + 7000 + 90000
Therefore, the expanded form of the number is 2 + 50 + 400 + 7000 + 90000

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Problem 3: 
Write the number 54276 in the expanded form?

Solution:

As given in the question,
The number is 54276
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
6 – ones
7 – tens
2 – hundreds
4 – thousands
5 – ten thousand
We write the numbers as
6 – 6 * 1
7 – 7 * 10
2 – 2 * 100
4 – 4 * 1000
5 – 5 * 10000
The expansion of the number is
(6 * 1) + ( 7 * 10) + (2 * 100) + (4 * 1000) + (5 * 10000)
6 + 70 + 200 + 4000 + 50000
Therefore, the expanded form of the number is 6 + 70 + 200 + 4000 + 50000

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Problem 4:
Write the number 827173 in the expanded form?

Solution:

As given in the question,
The number is 827173
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
3 – ones
7 – tens
1 – hundreds
7 – thousands
2 – ten thousand
8 – lakhs
We write the numbers as
3 – 3 * 1
7 – 7 * 10
1 – 1 * 100
7 – 7 * 1000
2 – 2 * 10000
8 – 8 * 800000
The expansion of the number is
(3 * 1) + (7 * 10) + (1 * 100) + (7 * 1000) + (2 * 10000) + (8 * 100000)
3 + 70 + 100 + 7000 + 20000 + 800000
Therefore, the expanded form of the number 82717 is 3 + 70 + 100 + 7000 + 20000 + 800000

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Problem 5:
Write the number 682472 in the expanded form?

Solution:

As given in the question,
The number is 682472
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
2 – ones
7 – tens
4 – hundreds
2 – thousands
8 – ten thousand
6 – lakhs
We write the numbers as
2 – 2 * 1
7 – 7 * 10
4 – 4 * 100
2 – 2 * 1000
8 – 8 * 10000
6 – 6 * 100000
The expansion of the number is
(2 * 1) + (7* 10) + (4* 100)+ (2*1000) + (8 * 10000) + (6 * 100000)
2 + 70 + 400 + 2000 + 80000 + 600000
Therefore, the expanded form of the number 682472 is 2 + 70 + 400 + 2000 + 80000 + 600000

---

Problem 6:
Write the number 5129693 in the expanded form?

Solution:

As given in the question,
The number is 5129693
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
3 – ones
9 – tens
6 – hundreds
9 – thousands
2 – ten thousand
1 – lakhs
5 – ten lakhs
We write the numbers as
3 – 3 * 1
9 – 9 * 10
6 – 6 * 100
9 – 9 * 1000
2 – 2 * 10000
1 – 1 * 100000
5 – 5 * 1000000
The expansion of the number is
(3 * 1) + (9 * 10) + (6 * 100) + (9 * 1000) + (2 * 10000) + (1 * 100000) + (5 * 1000000)
3 + 90 + 9000 + 20000 + 100000 + 5000000
Therefore, the expanded form of the number 5129693 is 3 + 90 + 9000 + 20000 + 100000 + 5000000

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Problem 7:
Write the number 146.963 in the expanded form?

Solution:

As given in the question,
The number is 146.963
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
3 – thousandths
6 – hundredths
9 – tenths
6 – ones
4 – tens
1 – hundreds
We write the numbers as
3 – 3 * \(\frac { 1 }{ 1000 } \)
6 – 6 * \(\frac { 1 }{ 100 } \)
9 – 9 * \(\frac { 1 }{ 10 } \)
6 – 6 * 1
4 – 4 * 10
1 – 1 * 100
The expansion of the number is
(1 * 100) + (4 * 10) + (6 * 1) + 9 * \(\frac { 1 }{ 10 } \) + 6 * \(\frac { 1 }{ 100 } \) + \(\frac { 1 }{ 1000 } \)
100 + 40 + 6 + 0.9 + 0.06 + 0.003
Therefore, the expanded form of the number 146.963 is 100 + 40 + 6 + 0.9 + 0.06 + 0.003

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Problem 8:
Write the number 58519 in the expanded form?

Solution:

As given in the question,
The number is 58519
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
9 – ones
1 – tens
5 – hundreds
8 – thousands
5 – ten thousand
We write the numbers as
9 – 9 * 1
1 – 1 * 10
5 – 5 * 100
8 – 8 * 1000
5 – 5 * 10000
The expansion of the number is
(9 * 1) + (1 * 10) + (5 * 100) + (8 * 1000) + (5 * 10000)
9 + 10 + 500 + 8000 + 50000
Therefore, the expanded form of the number 58519 is 9 + 10 + 500 + 8000 + 50000

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Problem 9:
Write the number 123.456 in the expanded form?

Solution:

As given in the question,
The number is 123.456
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
6 – thousandths
5 – hundredths
4 – tenths
3 – ones
2 – tens
1 – hundreds
We write the numbers as
6 – 6 * \(\frac { 1 }{ 1000 } \)
5 – 5 * \(\frac { 1 }{ 100 } \)
4 – 4 * \(\frac { 1 }{ 10 } \)
3 – 3 * 1
2 – 2 * 10
1 – 1 * 100
The expansion of the number is
(1 * 100) + (2 * 10) + (3 * 1) + (4 * \(\frac { 1 }{ 10 } \)) + (\(\frac { 1 }{ 100 } \)) + (\(\frac { 1 }{ 1000 } \))
100 + 20 + 3 + \(\frac { 4 }{ 10 } \) + \(\frac { 5 }{ 100 } \) + \(\frac { 6 }{ 1000 } \)
Therefore, the expanded form of the number 123.456 is 100 + 20 + \(\frac { 4 }{ 10 } \) + \(\frac { 5 }{ 100 } \) + \(\frac { 6 }{ 1000 } \)
The expanded form in the decimal format = 100 + 20 + 0.4 + 0.05 + 0.006

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Problem 10:
Write the number 181.813 in the expanded form?

Solution:

As given in the question,
The number is 181.813
To write the number in its expanded form, we have to find the units of the numbers and divide them by their multiple.
The units place of numbers are
3 – thousandths
1 – hundredths
8 – tenths
1 – ones
8 – tens
1 – hundreds
We write the numbers as
3 – 3 * \(\frac { 1 }{ 1000 } \)
1 – 1 * \(\frac { 1 }{ 100 } \)
8 – 8 * \(\frac { 1 }{ 10 } \)
1 – 1 * 1
8 – 8 * 10
1 – 1 * 100
The expansion of the number is
(1 * 100) + (8 * 10) + (1 * 1) + (8 * \(\frac { 1 }{ 10 } \)) + (1 * \(\frac { 1 }{ 100 } \)) + (3 * \(\frac { 1 }{ 1000 } \))
100 + 80 + 1 + \(\frac { 8 }{ 10 } \) + \(\frac { 3 }{ 100 } \) + \(\frac { 1 }{ 1000 } \)
Therefore, the expanded form of the number 181.813 is 100 + 80 + 1 + \(\frac { 8 }{ 10 } \) + \(\frac { 3 }{ 100 } \) + \(\frac { 1 }{ 1000 } \)
The expanded form in the decimal format = 100 + 80 + 1 + 0.8 + 0.03 + 0.001

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Do you have a question about geometrical shapes? If so, then you are at the right place and this article will guide you to know various types of geometrical shapes. Know various geometric shapes definitions with examples to make your preparation better. Follow different types of geometrical shapes their formulas, definitions, and examples. Check the properties of geometrical shapes in the further modules.

Geometrical Shapes – Introduction

The figures that demonstrate the shape of the objects are known as Geometric Shapes. These shapes have angles, boundary lines, and surfaces. Geometrical Shapes are of different types like 2D and 3D. Shapes are categorized with respect to uniformity or regularity. The regular shapes of the geometry will be symmetric most of the time like circles, squares, etc. A few of the shapes are freeform or organic shapes. For example, the shape of bush or creepers is organic or irregular.

In solid geometry, 3D shapes are cylinder, cone, cuboid, cube, and sphere. In-plane geometry, 2D shapes are closed figures and flat shapes like squares, circles, rhombus, rectangle,s, etc. We can observe the shapes example in our daily life like cones (conical), glasses (cylindrical), books(cuboid).

Geometry – Definition

The figures that demonstrate the shape of the objects are known as Geometric Shapes. 2D figures lie on the X and Y axis but 3D figures lie on the X, Y, and Z-axis. X and Y-axis show length and breadth whereas Z shows the object’s height. To draw the figures we have to start with the line segment or line or a curve. Based on the arrangements or number of lines, we will get different shapes like a triangle, pentagon, etc.

Types & List of Geometric Shapes

Two Dimensional Shapes	Three Dimensional Shapes
Circle
Triangle
Semi-Circle	Cube
Square	Sphere
Rectangle	Cone
Rhombus	Cuboid
Parallelogram	Cylinder
Kite
Trapezium
Polygons (Octagon, Nonagon, Pentagon, Hexagon, Decagon, etc.)

Quick Links

Fundamental Concepts of Geometry	Geometrical Design and Models
Points, Lines, and Shapes	Some Geometric Terms and Results
Triangle	Nets of Solids
Types of Lines

Types and Properties of Geometric Shapes

As mentioned above there are various types of geometric shapes. The properties of those shapes are as follows:

Circle

The circle is the shape of the geometry that has no straight lines. The combination of curves gives the circle which are all connected. There are no angles in the circle. There are various terms involved in the circle. They are:

Radius:
Radius is considered as the distance between the center and any point on that circle.

Diameter:
The diameter is the line that passes through the center and meets at any points on the circle.

Chord:
The longest line meets at any point on the circle. The longest chord is known as the diameter of the circle.

Circumference:
The boundary of the circle where the length of the closed curve will form the boundary is called the circumference of the circle.

Triangle

The polygon with three sides, three edges, and three vertices is known as a triangle. The sum of the internal angles of a triangle is 180°. Triangle is made up of three connected line segments and angles will be of distinct measurements. There are various triangles depending on the angles found in the triangle itself. For suppose, if one side of the triangle is a right angle, then the triangle is known as a right-angle triangle.

Types of Triangles

Scalene Triangle
All the side lengths with different measurements are known as a scalene triangles. In this triangle, no two sides will be of equal length.

The above figure shows that no two sides have an equal length which is a scalene triangle.

Equilateral Triangle
The triangle which has a length of equal sides is called an equilateral triangle. This triangle will have all the angles equal to 60° and 3 lines of symmetry.

The above figure shows that all the sides of the triangle are equal.

Isosceles Triangle
The triangle with 2 equal angles and 2 sides of equal length is known as the isosceles triangle. All these triangles will have a line of symmetry.

The above figure shows that both the angles and sides are equal.

Right Triangle
The triangle with one angle of 90° is called the right-angled triangle.
The above figure shows that one of the angles is 90° which is a right triangle

Obtuse Triangle
The triangle with one angle greater than 90° is known as an obtuse triangle. The other two angles of the triangle are acute which are less than 90°.

The above figure shows that one angle is greater than 90° which is an obtuse triangle.

Acute Triangle
The triangle with all sides as acute(less than 90°) is known as an acute triangle.
The above figure shows that all the angles are less than 90° which is an acute angle triangle.

Semi Circle

The semicircle is defined as a half-circle that is formed by cutting the complete circle into two equal halves along the diameter line. The semicircle has one line of symmetry which is the reflection of that symmetry. From the above-given figure, r is the radius of the semicircle.

Square

The square is defined as a closed, two-dimensional figure with 4 equal sides. It is a quadrilateral. For suppose, we can find the square shape in the chessboard or a slice of bread.

Rectangle

The polygon with four sides having the internal angles equal to 90° is known as a rectangle. Two sides of the rectangle at each vertex or corner meet at right angles. The main difference between square and rectangle is that rectangle will have two opposite sides of the same length.

Rhombus

The flat-shaped 4 equal straight sides figure is known as a rhombus. Generally, a rhombus looks like a diamond that has all sides of equal length. In a rhombus, opposite angles are equal and opposite sides are parallel.

Parallelogram

The 2-dimensional geometric shapes whose opposite sides are parallel to each other is known as a parallelogram. This is a type of polygon which have four sides where the pair of the parallel sides are in equal length. The opposite interior angles of the parallelogram are equal .

Trapezium

A 2D-shaped type of quadrilateral with only two parallel sides is called a trapezium. The two sides of the trapezium are parallel and the other two sides are non-parallel. The trapezium has four sides and four vertices, they are either simple or complex.

Polygons

The polygons are the plane figures which are described with the finite number of straight lines connected to form the closed polygon circuit or polygon chain.

Cube

In geometry, a cube is a 3-dimensional object which is bounded by six square facets, faces, or sides which are meeting at each vertex. It has 12 edges, 6 faces, and 8 vertices.

Sphere

A 3D geometrical object which has a surface like a ball is known as a sphere. Alike a circle, the sphere is considered as the set of points that are all at the same distance r from the point in 3D space.

Cone

The cone is the figure formed by using a set of lines or line segments that connects the common point named vertex or apex. The height of the cone is determined as the distance from the base to the vertex of the cone.

Cuboid

A 3D shape with six faces is known as a cuboid and it forms a convex polyhedron. The cuboid faces can be quadrilateral and 6 rectangles are required to make a rectangular cuboid that is placed at right angles.

Cylinder

The cylinder is the most basic curved 3D geometric shape with the surface formed from the line segment to the surface formed by points which are known as the axis of the cylinder.

Thus, these are the various geometric shapes we use in our day-to-day life.

Make your kids even more interested in Math Activities by taking help from our fun-learning Kindergarten Math Curriculum, Worksheets, Activities, Problems, Fun Games

Confused about Points and Line Segment? Don’t worry! Here we are providing the complete details regarding  Points and Line Segments. Know what is the relationship between a point and a line segment. Follow the various trips and facts to remember points and line segments. Get the information regarding definition, differences, types, and examples of points and line segments in the further sections.

Points and Line Segment – Introduction

Before going to the deeper concepts we will know about point and line segments.

What is a Point?
A point generally depicts a location in any plane. The plane can be 2 – Dimensional, 3 – Dimensional or of any Dimension.
This is the general definition of a point. In the more modern world, the point can be considered as an element in a space. A point does not have length, width, or thickness.

Properties of a Point:

• The point will not have the length, height, shape, and size.
• Point marks as the beginning to draw the figure or shape.
• The point which is marked is labeled with capital letters.

Types of Points

There are different types of points in our general mathematics.

Collinear Points:
One or more points lying on a straight line are known as collinear points.

In the above figure, A, B, C, and D are the points that are lying on the straight line. Hence, these points are known as collinear points.

Non-Collinear Points:
If three or more points cannot be joined with a straight line, then those points are known as non-collinear points.

In the above figure, P, Q, R, and S are the points that are not lying on the straight line. Hence, these points are known as non-collinear points

Concurrent Points:

If two or any number of straight lines meet at a single point, then that point is known as a concurrent point.
The straight lines AB, CD, EF are meeting at a point which are known as concurrent points.

What is a Line Segment?
The Line Segment is a part of a line that has some boundaries. The Line Segment is a line that may be bounded between two endpoints.

Properties of Line Segment:

• The line segment will have two endpoints and all the points are present between them.
• The representation of line segments depends on the type of line segments.
• If the line segment is closed one, then it is represented with two points.
• If the line segment is an open one, then it is represented with two arrows.

Types of Line Segments

There are different types of line segments in our general mathematics.

Closed Line Segment:
The first one is the closed line segment. This is the line segment that is bounded between two endpoints. The endpoints are mentioned by using points. So, here the point is the element that divides a line to form a Line Segment.

Open Line Segment:
Another one is the open line segment. This is the line segment that has no endpoints. The ends of the line are mentioned by using either > or <. These explain that the line is extended on both ends. So, it is a continuing line segment that has an infinite length on both sides until it is stopped by a point.

Semi-Open Line Segment:
The last one is the semi-open line segment. This kind of line segment has one endpoint at one end and no endpoint at another end. This shows us that one end is a closed line segment and another end is an open line segment. So, it is a continuing line segment at one end and a fixed-line segment at another end that has an infinite length on one side until it is stopped by a point.

Difference between a Point and a Line Segment

Point	Line Segment
Point is an element in a space that gives the exact location in some particular space	The line segment is a line that has some boundaries where every point in that line lies within the boundaries
The point has no length, width, or thickness	The line segment length is indefinite and it has some thickness
Point is represented with “.”	The line segment is represented with “—”
Difficult to define the length, with and thickness for a point	The length of a line segment may be ranging from millimeters (mm) to Kilometers(km)

Read More Articles

Nets of Solids	Triangle	Types of Lines
Some Geometric Terms and Results	Geometrical Design and Models	Points, Lines, and Shapes

Point and Line Segment Examples

Problem 1:
Consider CX is a line segment in a One Dimensional Plane. Where C is 0 and X is 5. Show whether 3 lies in this line segment, length of the line segment and define the type of line segment.

Solution:
Given,
CX is the given line segment where C is 0 and X is 5.
3 lies between 0 and 5. So, 3 is a point in the line segment CX such that the point is 3 places from C and 2 places from X.
The Lenght of CX is 5. It has 2 endpoints so the type of line segment is a closed line segment.

Problem 2:
x=y is a line starting from the origin in a 2 Dimensional Plane. State whether (3,3) lies on the line and check the type of line segment.

Solution:
Given,
x=y is a line segment

It is a 2 Dimensional plane. So, The point is represented as (0,0).
From the figure, we observe that line x=y passes through the point (3,3).
Therefore, (3,3) lies on the line x=y.
Here, one end of the line has a point and the other end does not. So, it is a Semi-open type of Line Segment.

Problem 3: x=0 is a line in a 2 Dimensional Plane. State whether (0,-3) lies on the line and check the type of line segment.
Solution:
Given,
x=0 is a line segment

-3 lies 3 units to the left of the origin on the line x=0.
Therefore, (0,-3) lies on the line segment x=0.
Here, both the ends of the line have no endpoints and can be extended in both directions till infinity.
So, this is an Open type of Line Segment.

Know the fundamental concepts of Geometry here. We are providing detailed information regarding point, plane, ray, line segment, incidence properties of lines in a plane, collinear points, concurrent lines, two lines in a plane, etc. Follow the important points and basics of geometry. Go through the below sections to know the formulas, examples of all the basic geometry concepts.

Fundamental Concepts of Geometry – Introduction

The term “Geometry” is derived from the Greek word “Geometron” where Geo means “Earth” and Metron means “Measurement”. Geometrical ideas are basically reflected in various forms of engineering, architecture, art, measurements, etc. Different objects have different shapes where the ball is round in shape and the ruler is straight. Know some of the interesting facts that enable us to learn more about shapes around us.

Geometry is basically divided into two types such as solid geometry and plane geometry. There are certain formulae for measuring all the geometric concepts. The basic geometric concepts are as follows:

Point

Point is considered as the fundamental object in euclidean geometry. It determines the location which has no length, breadth, and thickness. The small dot marked by pencil or pen on a paper or sheet made by a fine needle is few examples of a point. It is represented with (.). Every point has to be denoted with a name and we have to use a single capital letter for it. Representation of points of A, B and M are as follow:

Lines

The basic concept of a line is its straightness which can indefinitely extend in both ways or directions. The 2 arrowheads placed in opposite directions indicate that the line length is unlimited. The line has only length but not thickness or breadth which has no endpoints. Lines are made up of an infinite number of points. Lines also must have names as the points do, therefore we can refer to them easily. Lines are represented with (↔). If a line is passing through the points A and B, then it is denoted with line notation of AB ↔ and graphically represented as:

Plane

Planes are nothing but flat surfaces. The plane has length and breadth but not thickness. The basic concept of the plane is its flatness and it extends in all directions indefinitely. The length and breadth of the plane are always unlimited and are two-dimensional. The plane is made up of an infinite amount of lines and two-dimensional figures are called plane figures. All the lines and points which lie on the same plane are known as coplanar. Plane in graphical representation is represented as:

Line Segment

The line segment is the portion of a line between the points. Two or more line segments are said to be equal if and only if they have the same length. If two lines are parallel, then their line segments are said to be in parallel. If the length of the line is infinite, we use a part of the line where the line segment connects both the endpoints. The line segment with both endpoints A and B are denoted with the line segment notation AB —.

The line segment will be drawn as part of the line.

Ray

The line of unlimited length and one end is called the ray. The unlimited number of rays can be drawn with the initial point. If there are two rays with similar initial point and extending in opposite direction are called as opposite rays. Two rays are said to be in parallel if and only if the lines between them are parallel. The ray that is starting from A and passing through B is denoted by AB→

Angles

The angle is a combination of both rays with the common endpoint. The angle is represented with the symbol “⌊”. The point of the corner at an angle is called the vertex. The angle contains two straight sides which are called the arms of the angle.

How to Measure Angles?

The angle consists of 2 rays with the common endpoint. Both rays are known as the sides of the angle and the common endpoint is the angle vertex. For each angle that is rotated about the vertex will have a measure which is determined by terminal side rotation about the initial side. If it is rotated counterclockwise, it generates the positive angle measure and a clockwise rotation generates the negative angle measure.

Angles are measured in units called radians or degrees. Angles are classified into various types based on the measure: right angle, obtuse angle, acute angle, straight angle

There are specific conditions for the angles like

• If two positive angles measure a sum of 90°, then the angles are called complementary angles
• If two positive angles measure a sum of 180°, then the angles are called supplementary angles

Difference between Line Segment, Line and Ray

Line Segment	Ray	Line
Line Segment is the part of the line with two fixed points	Ray is the part of the line with one infinite end and one fixed starting point	The line can be drawn on a plane with o fixed endpoints
Line Segment can be drawn on the piece of the paper	Ray cannot be drawn on the paper and can be represented in the diagram only	The line cannot be drawn on the paper and can be represented in the diagram only
The length of the line segment is definite so it can be measured	The length of the ray cannot be measured as one of its ends is indefinite	The length of the line cannot be measured as one of its lengths is indefinite
Line Segment can be represented with AB—	Ray can be represented with AB→	The line can be represented with AB↔
Symbol of Line Segment is ⋅—⋅ with 2 dots which are at the either ends to indicate that they are fixed	The symbol of Ray is ⋅—> with 1 dot at the starting and an arrowhead to indicate it and goes in the other direction	Symbol of Line is <—> with two arrow marks at either ends to indicate they go in both directions

Collinear Points

Two or more points that lie on the same line in the plane are known as collinear points.

• Here the line is known as the line of colinearity.
• Both the points are always collinear.

In the above diagram,

Points A, B, and C are the points collinear lying on a line.

X, Y, and Z are not collinear points because those three points do not lie on the same line. Therefore, they are non-collinear points.

In the above diagram M, N, O, P, Q are collinear points and A, B are non-collinear points.

Quick Links

Nets of Solids	Triangle	Types of Lines
Some Geometric Terms and Results	Geometric Design and Models	Points, Lines, and Shapes

Incidence Properties of a Line in a Plane

If a point is given in a plane, then an infinite number of lines can be drawn to pass through it. With the given point in the plane, infinitely many lines can be drawn to pass through it.

Two clear points in the plane will determine the unique line. Only one line can be drawn to pass through the given points and the line lies in the plane completely.

An infinite number of points will lie on a similar plane.

Two lines in the plane will either intersect or are parallel to each other.

Concurrent Lines

Three or more lines that pass through the same point are known as concurrent lines and the common point of the line is called the point of concurrency.

In the above figure p, q, r, s, t, u meet and intersect at the point O which are called concurrent lines.

Geometric Theorems

The Triangle Angle Sum Theorem 
All the interior angles of a triangle will have the sum of 180°

The (OAT) Opposite Angle Theorem
The opposite angles are equal, if two straight lines cross

Parallel Lines Theorem
If the parallel lines are cut by the transversal
a) alternate angles will be equal (PLT – Z)
b) corresponding angles will be equal (PLT – F)
c) interior angles will have the sum of 180° (PLT – C)

Feeling tricky about numerators and denominators? Get a clear idea about this concept by following the simple tricks mentioned below. You can get the perfect solution to the question of how to find the numerator and denominator of a fraction. Know the general representation of the numerator and denominator in the further modules. Follow the definitions, examples, frequently asked questions, etc.

Numerator and Denominator

Once you notice a fraction, you will come to know that there are two numbers involved in a fraction which are the top number and the bottom number. Have you ever wondered what these numbers are and what do they represent? These numbers are called the numerator and denominator. The easy and the simplest way to represent the numerator and denominator is:

Numerator: the fraction’s top number
Denominator: the fraction’s bottom number
If \(\frac { a }{ b } \) is a fraction, then a is called the numerator and b is called the denominator.
Example:
If the fraction value is \(\frac { 7 }{ 4 } \), the top number is 7 and the bottom number is 4. Therefore, the numerator value is 7 and the denominator value is 4.
If the fraction value is \(\frac { 3 }{ 10 } \), the top number is 3 and the bottom number is 10. Therefore, the numerator value is 3 and the denominator value is 10.

What do Numerator and Denominator Represent?

The fraction value represents the part of a whole. The denominator in the fraction represents the equal number of parts in the whole and the numerator in the fraction represents the number of parts that are being considered.

If the fraction is in the form of \(\frac { a }{ b } \), then the numerator “a” is the whole object which is divided into “b” parts of equal size which is known as denominator.

Read more Related Articles:

• Fraction as a part of Whole
• Fractions
• Like and Unlike Fractions

What is Numerator?

The numerator is the number value that appears on the top portion of the fraction. As discussed in the above sections, the numerator is part of a whole. Hence, the numerator resembles the equal parts of a number in the whole which is considered.
For suppose, the fraction is \(\frac { 5 }{ 10 } \) which means that the numerator 5 parts of the whole object divided into 10 equal parts or sizes that is taken into consideration.

To understand this concept more clearly, let us consider an example of pizza. We divide the pizza into 8 pieces to distribute it amongst 8 people at the party comprising of 5 boys and 3 girls. Therefore, we say that \(\frac { 5 }{ 8 } \) part of the pizza has been taken by boys. Also, \(\frac { 3 }{ 8 } \) part of the pizza is left for the girls.

What is a Denominator?

The denominator is the number value that appears on the bottom portion of the fraction. It represents the equal number of parts that can divide the whole.

For suppose, the fraction is \(\frac { 1 }{ 2 } \) which means that two equal parts of one object are considered. To understand the concept more clearly, we will consider the example the same as above. We divide the pizza into 8 pieces to distribute it amongst 8 people at the party comprising of 5 boys and 3 girls. Therefore, we say that \(\frac { 1 }{ 8 } \) piece of 1 whole pizza is divide into 8 people.

Numerator and Denominator Examples

Examples of Numerators
Some of the examples of the numerator are,

Fractions	Numerators
x/2y	x
11/2	11
5/10	5
4x/6	4x
17/7	17

Examples of Denominators
Some of the examples of the denominators are:

Fractions	Denominators
x/2y	2y
11/2	2
5/10	10
4x/6	6
17/7	7

Fun Facts about Numerator

• If the value of the numerator is 0, then the entire fraction becomes zero irrespective of the denominator value. For suppose, \(\frac { 0 }{ 21 } \) is 0, \(\frac { 0 }{ 32 } \) is 0 and so on.
• The derivation of numerator word is from Latin language “numerator” which gives the meaning as a counter.
• If the numerator value is same as the denominator value, then the resultant fraction value becomes 1. For suppose \(\frac { 24 }{ 24 } \) is 1, \(\frac { 2 }{ 2 } \) is 1

Fun Facts about Denominator

• The value of the denominator cannot be zero, if the denominator value is 0, then the fractions become undefined.
• If the denominator value is same as the numerator value, then the resultant fraction value becomes 1. For suppose \(\frac { 24 }{ 24 } \) is 1, \(\frac { 2 }{ 2 } \) is 1

Example Problems

Problem 1:
Identify the numerator and denominator in the fraction \(\frac { 3 }{ 4 } \)?
Solution:
As given in the question,
The fraction is \(\frac { 3 }{ 4 } \)
As we know, the top number is the numerator, from the fraction 3 is the numerator value.
The bottom number is the denominator, therefore from the fraction 4 is the denominator value.

Problem 2:
Identify the numerator and denominator in the fraction \(\frac { 32 }{ 24 } \)?
Solution:
As given in the question,
The fraction is \(\frac { 32 }{ 24 } \)
As we know, the top number is the numerator, from the fraction 32 is the numerator value.
The bottom number is the denominator, therefore from the fraction 24 is the denominator value.

Problem 3:
Identify the numerator and denominator in the fraction \(\frac { 54 }{ 10 } \)?
Solution:
As given in the question,
The fraction is \(\frac { 54 }{ 10 } \)
As we know, the top number is the numerator, from the fraction 54 is the numerator value.
The bottom number is the denominator, therefore from the fraction 10 is the denominator value.

FAQs on Numerator and Denominator

1. Define Numerator?

The numerator is defined as the number above the horizontal line of the fraction which acts as a dividend of the denominator. The numerator is the top number in the fraction which represents the number of parts of a whole.

2. Define Denominator?

The denominator is defined as the number below the horizontal line of the fraction which acts as a divisor of the numerator. The denominator is the bottom number in the fraction which represents the total equal parts of an object that is divided into.

3. Is the denominator the top or bottom number?

The denominator is the bottom number of the fraction which shows the equal parts the item is divided into.

4. What is the difference between numerator and denominator?

In the fraction, the top number is called the numerator and the bottom number is called the denominator. For suppose, \(\frac { 1 }{ 2 } \) is the fraction. Here, 1 is the numerator and 2 is the denominator. Therefore, the numerator defines the number of parts we have and the bottom number defines the number of equal parts it is divided into.

Confused about the concept of finding time in simple interest? Here, we are providing detailed information to find time when principal interest and rate are given. Follow the time definition, formula, and conversion of months and days into years to solve simple interest problems, etc. Check the later modules to know the examples and step-by-step procedure to solve the time problems when principal, interest, and rate are given.

To find Time when Principal Interest and Rate are given

Time in simple interest is considered as the starting period when the money is borrowed to the period of time by which the money should be returned with the additional amount of interest. It is also called the deadline or term.

To explain it in clear, we consider an example, Maria was doing her Masters and she was in lack of money, so she thought of taking the student loan of $20,000 from the bank. The interest rate for the loan is 4% and the interest amount she has to pay by the end of term is $8000. The time period by which she has to repay the loan is 5 years which is known as time.

Apart from loans, the time period is also valid for deposits, investments, borrows etc. For example, If Maria opens a fixed deposit for a fixed tenure of 10 years. Then the tenure is known as the time period.

Time Formula when Principal, Interest, and Rate are given

In the above example of Maria’s student loan, we know the time period and we use it to find the simple interest. Consider that we know the principal amount, interest amount, and rate of interest we have to calculate the time period, As we know the interest formula I = P * R * T / 100, we have to rearrange to find the time period.

Therefore, the time can be written as
T = (100 * I) / (P * R)
in which T is the time and equals 100 and interest divided by the principal amount and rate of interest.

Let us consider an example of finding the time period of the loan where the principal amount is $6000, the interest amount is $3600 and the rate of interest is 6%

To solve the above calculations, we have to substitute the values in the equation, T = (100 * I) / (P * R)
T = (100 * 3600) / (6000 * 6)
T = 360000 / 36000
T = 10 years
Therefore, the time is 10 years

Read More Articles

What is Simple Interest	Worksheet on Simple Interest	Worksheet on Factors Affecting Interest
Simple Interest when time is given in months and days	To find Rate when Principal Interest and Time are given	To find Principal When Time Interest and Rate are Given

How to Calculate Time in Simple Interest?

You have to follow a few steps to calculate time in simple interest. The steps are as follows:
Step 1: Understand the question properly
Once you know the question, understand it clearly and know the terms included in it. We know the equation as,
T = (100 * I) / (P * R)
T is the time period(year/month)
I is the interest amount paid for year/month
P is the principal amount
R is the rate of interest
Step 2: Determine the Principal amount
In the first step, you have to determine the principal amount. Before calculating the time period, you must know the principal amount by which the interest rate will grow. It is the amount that is initially credited or invested.
Step 3: Determine the interest rate
Next, you have to determine the interest rate. If the interest rate is in decimal value, then you have to convert it to percentages by multiplying it by 100. For suppose, you took $5000 from your friend and agreed upon the interest of 6% and the interest amount is $150. Then 6% is the interest rate.
Step 4: Determine the interest amount
You have to find the interest amount also. As given in the above example, the interest amount is $150.
Step 5: Substitute the values in the equation
As we know the equation, T = (100 * I) / (P * R). Substitute all the values of principal, interest rate and interest amount in the equation.
As given in the above example, the values are
P = $5000
I = $150
R = 6%
The equation is,
T = (100 * I) / (P * R)
T = (100 * 150) / (5000 * 6)
T = 15000 / 30000
T = 0.5 years

Conversion of Years into Months and Days

If we get the time period in years and want to convert it into months or days, then there is a technique to follow. If you want to convert the time into months, then you have to multiply it by 12 and if you want to convert it to days, then you have to multiply it by 365, then you get the desired time period in months or days.

For example, you took $5000 from your friend and agreed upon the interest of 6% and the interest amount is $150. Then 6% is the interest rate. Find the time period in months?
As given,
P = $5000
I = $150
R = 6%
The equation is,
T = (100 * I) / (P * R)
T = (100 * 150) / (5000 * 6)
T = 15000 / 30000
T = 0.5 years
To find the time in months, we have to multiply it with 12
Therefore, time = 0.5 * 12 = 6
Hence, the time period is 6 months

Example Problems to find Time When Principal, Interest and Rate are Given

Problem 1:
At what time will a loan of $6500 generate a simple interest of $1300 at the rate of 2.5%?
Solution:
As given in the question,
Principal, P = $6500
Simple Interest, I = $1300
Rate of Interest = 2.5%
As we know the formula,
T = (100 * I) / (P * R)
T = 100 * 1300 / 6500 * 2.5
T = 130000 / 16250
T = 8
Therefore, the time period is 8 years

Problem 2:
In how much period of time would Rs. 11,500 become Rs. 14,605 at a Simple Interest rate of 9% per annum. Define the time period in days?
Solution:
As given in the question,
Principal P = 11,500
Amount A = 14,605
Rate = 9%
Amount = SI + P
14605 = SI + 11500
SI = 3105
As we know that,
SI = P * R * T / 100
T = SI * 100 / P * R
T = 3105 * 100 / 1500 * 9
T = 3 years
To convert years into days, we have to multiply it with 365
T = 3 * 365
T = 1095
Therefore, the time period is 1095 days

Problem 3:
In how much time will Rs. 1200 mount to Rs. 1726 at 9% per annum simple interest. Find the time period in months?
Solution:
As given in the question,
Amount A = 1726
Principal P = 1200
Rate R = 9%
Simple Interest = Amount – Principal
SI = 1726 – 1200
SI = 526
We know that,
Time = 100 * SI / P * R
T = 100 * 526 / 1200 * 9
T = 52600 / 10800
T = 4.8 years
To convert the time of years into months, multiply it with 12
T = 4.8 * 12
T = 57.6 months
Therefore, the time period in months = 57.6 months