CBSE Class 10th Maths Real Numbers

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• published: 03 Nov 2014
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CBSE Class 10 X maths real numbers video lectures for NCERT. With NCERT exercise solutions. In this video, we will be learning about real numbers. Earlier in class 9th, we have already learned about real numbers. Real numbers are made up of 1,2,3,4,5,6,7,8,9,0 and decimal. Real numbers can be a positive integer, negative integer, rational number, or an irrational number. In the video, we have discussed two important properties of positive integers, 1. Euclid’s division algorithm 2. Fundamental theorem of arithmetic Before we discuss these two, first let us understand what is an algorithm? Algorithm nothing is but a series of well-defined steps which gives a process to solve a problem. Next, we have discussed Euclid’s division lemma. So what is a lemma? The lemma is nothing but a proven statement used for proving other statements. According to this Lemma, For given positive integers a and b there exists a unique integer q and r such that it satisfies the relation a= bq+ r (q = quotient and remainder) This lemma is basically used to compute HCF of two positive integers? Now, what is HCF? HCF stands for Highest Common Factor and is the highest positive integer dividing a, b and thus is called HCF of a and b. Further, in the mathematics video, we have discussed Euclid’s division algorithm followed by Fundamental Theorem of Arithmetic. This theorem is related to the multiplication of positive integers. There are 2 uses of this theorem, 1. To prove the irrationality of√(2,) √3, etc. 2. To know which rational number is terminating and which is not terminating or repeating. According to this theory, We can express or factorize every composite number as a product of prime numbers and this way factorization is unique. This is apart from order in which prime factor occurs. This theorem is also used in prime factorization method. Further, in the video, we have revisited irrational numbers. We have discussed and proved many theorems in the above mathematics video. Few of the theorem discussed is, 1. Let p is a prime number and p divides a2 then p will also divide a. ( a= positive integer) 2. Prove √(2 ) is irrational This theorem is well explained using detailed steps so that you don’t get confused at any part of the proof. In the end of the video, we have discussed rational numbers and their decimal expansions. Rational numbers can be of two types, 1. Terminating numbers- 6.34, 73.34, 63.23 2. Non – terminating repeating – 7.38779..., 83.3948... Basically, in this chapter, we will explore when the decimal expansion of p/q (q ≠0) is terminating or non – terminating repeating. The video ends with a theorem which explains this. Video lectures for iit jee mains and advanced. 700 hrs. hd video content for jee. Visit https://www.iitjeemaster.com for more videos. Install our app for all videos. https://play.google.com/store/apps/details?id=com.iitjeemaster.myvideo channel https://www.youtube.com/user/iitjeemaster call 08226060233 ,09977204422