LESSON PLAN CLASS 10th SUBJECT MATHS TIME: 35min. Name of the topic REAL NUMBERS Sub topic Determining the Nature of The Decimal Expansions of Rational Numbers Time Management 1. 2. 3. 4. 5. P K Testing Motivation Presentation Student.
Download ReportTranscript LESSON PLAN CLASS 10th SUBJECT MATHS TIME: 35min. Name of the topic REAL NUMBERS Sub topic Determining the Nature of The Decimal Expansions of Rational Numbers Time Management 1. 2. 3. 4. 5. P K Testing Motivation Presentation Student.
Slide 1
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 2
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 3
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 4
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 5
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 6
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 7
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 8
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 9
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 10
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 11
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 12
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 2
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 3
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 4
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 5
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 6
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 7
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 8
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 9
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 10
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 11
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
•
•
•
•
•
Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
•
•
•
•
0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
•
•
•
•
•
•
•
•
•
•
•
•
•
Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)
Slide 12
LESSON PLAN
CLASS 10th
SUBJECT MATHS
TIME:
35min.
Name of the topic
REAL NUMBERS
Sub topic
Determining the Nature of The Decimal
Expansions of Rational Numbers
Time Management
1.
2.
3.
4.
5.
P K Testing
Motivation
Presentation
Student Activity
Evaluation & Conclusion
3 minutes.
2 minutes.
12 minutes.
10 minutes.
8minutes.
GENERAL OBJECTIVES
• At the end of the lesson students will enable
to:
• 1.Understand terminating decimal expansions.
• 2. Understand non-terminating repeating
expansions.
SPECIFIC OBEJECTIVES
• students can differentiate terminating and
non terminating repeating decimal
expansions.
Previous knowledge testing
Teacher:-Dear students ,what is a rational
number?
Students: 2/5 a rational number ?
T:-Change it into decimal expansion.
S: - 2/5=0.4
T:- Change 1/8 into decimal expansion.
S:- 1/8=0.125
T: -Change 1/3 into decimal expansion.
S:- 1/3=0.3333……………
INTRODUCTION OF THE TOPIC
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Dear students , as you know that 2/5=0.4 and 1/8=0.125
These are the terminating decimal expansions.
To understand this topic Let us consider the following examples
0.4=4/10=4/101
0.125=125/1000=125/103
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0.375=375/1000=375/103
0.1025=1025/10000=1025/104
As we know that 2 and 5 are the only prime factors of 10
Any positive integral power of 10, say10n can be expressed
contd
as2nx 5n
• Therefore if the numerators and denominators are co-prime and denominator are
in the form of 2mx5n then the rational numbers having terminating decimal
expansions.
• For examples:• (1) 1.512=1512/103=23x33x7/23x53=33x7/53=189/20x53
• (2) 27.7624=277624/104=23x32x7x531/24x54=32x7x531/2x54=33453/21x54
• From the above discussion that the denominators of the rational numbers having
terminating decimal expansions are expressible in the form 2mx5n
Conclusion:-If x be a rational number whose
decimal expansion terminates. Then x can
expressed in form p/q, where p and q are coprime , and the prime factorisation q is in the
form 2mx5n, where m, n are non negative
integers.
Let us now consider the following rational numbers:(1) 1/3=0.33333…………
(2) 5/3=1.6666……….
(3) 1/7=0.142857142857…….
The above rational numbers are non terminating and repeating.
These numbers numbers are non terminating and repeating because the
denominators of these rational numbers are not in form of 2mx 5n
Conclusion:- If x =p/q be a rational number,
such that the prime factorisation of q is not
of the form 2mx 5n where m,n are non
negative integers. Then x has a decimal
expansion which is non-terminating
repeating.
STUDENT ACTIVITY
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Without long division , state whether the following rational numbers having
terminating decimal expansion or a non-terminating repeating decimal
expansion:
Group1 : 23/8
125/441
15/1600
3/320
Group2 : 13/3125
77/210
29/343
2/15
Group3: 17/6
189/125
49/500
15/525
Home Assignment
• Every students should write any ten rational
numbers and determine the nature of the
decimal expansions.
Prepared by
1.sh. Bhagat Singh (lecturer in Maths.) GSSS Tangling Distt. Kinnaur ( H.P.)
2.sh. Roop Singh (Lect.in Maths.) GSSS Randhara Distt. Mandi (H.P.)
3.sh. Lalit kumar (Lect.in Maths.) GSSS nagwain Distt. Mandi (H.P.)
4.sh. Yograj (Lect.in Maths.) GSSS Baryara Distt. Mandi (H.P.)
5.sh. Satya Prakash sharma (Lect.in Maths.) GSSS Dehar Distt. Mandi (H.P.)
6.sh. Bhim Singh Thakur (Lect.in Maths.) GSSS Drang Distt. Mandi (H.P.)
7.sh. Kamal Kishore (Lect.in Maths.) GSSS Mahadev Distt. Mandi (H.P.)
8.sh.Pawan Kumar (Lect.in Maths.) GSSS Sihunta Distt. Chamba (H.P.)
9.sh. Om Prakash (T.G.T) GSSS Chandi Distt. Solan (H.P.)
10.sh. Dheeraj Vyas (Lect. In Maths) GSSS Khalet Distt. Kangra (H.P.)