Presentation on theme: "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."— Presentation transcript:
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. P K Testing 3 minutes. 2. Motivation 2 minutes. 3.Presentation 12 minutes. 4.Student Activity10 minutes. 5. Evaluation & Conclusion 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=4/10 1 0.125=125/1000=125/10 3 0.375=375/1000=375/10 3 0.1025=1025/10000=1025/10 4 As we know that 2 and 5 are the only prime factors of 10 Any positive integral power of 10, say10 n can be expressed as2 n x 5 n contd
Therefore if the numerators and denominators are co-prime and denominator are in the form of 2 m x5 n then the rational numbers having terminating decimal expansions. For examples:- (1) 1.512=1512/10 3 =2 3 x3 3 x7/2 3 x5 3 =3 3 x7/5 3 =189/2 0 x5 3 (2) 27.7624=277624/10 4 =2 3 x3 2 x7x531/2 4 x5 4 =3 2 x7x531/2x5 4 =33453/2 1 x5 4 From the above discussion that the denominators of the rational numbers having terminating decimal expansions are expressible in the form 2 m x5 n 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 2 m x5 n, 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 2 m x 5 n Conclusion:- If x =p/q be a rational number, such that the prime factorisation of q is not of the form 2 m x 5 n 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.