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**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

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**Time Management 1. P K Testing 3 minutes. 2. Motivation 2 minutes.**

3. Presentation minutes. 4. Student Activity 10 minutes. 5. Evaluation & Conclusion 8minutes.

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**GENERAL OBJECTIVES At the end of the lesson students will enable to:**

1.Understand terminating decimal expansions. 2. Understand non-terminating repeating expansions.

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SPECIFIC OBEJECTIVES students can differentiate terminating and non terminating repeating decimal expansions.

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**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……………

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**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 as2nx 5n contd

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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) =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 co-prime , and the prime factorisation q is in the form 2mx5n, where m, n are non negative integers.

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**Let us now consider the following rational numbers:-**

(1) 1/3= ………… 5/3=1.6666………. 1/7= ……. 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.

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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

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Home Assignment Every students should write any ten rational numbers and determine the nature of the decimal expansions.

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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.)

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