All numbers can be classified into two categories Ch 10 Maths Class 10 Extra Questions Us -- Real and Imaginary. A real number can be actually perceived and can be represented in a number line. It includes all integers -- positive and negative, all natural numbers 1, 2, 3, �. An imaginary number on the other hand cannot be perceived. Square root of all negative numbers is imaginary. A real number can be represented as an infinite decimal expansion. A real number can be rational or irrational.
All rational numbers and all irrational numbers Ch 10 Maths Class 10 Extra Questions Us together make a group of real numbers. A rational number an be written in the form p qboth p and Ch Questions 10 Maths 10 Us Class Extra q being integers q 0 while an irrational number Ch 10 Maths Class 10 Extra Questions Us can not be impressed in such a way. The Ch 13 Maths Class 10 Extra Questions Guide decimal expansion of a rational number say x can terminate after a finite number of digits.
On the other hand in case of an irrational number, the decimal expansion continues without repeating. Ex: 1. First, let us understand the meaning of Lemma and Algorithms. A Lemma is a minor proven statement which is used to prove other statements.
An algorithm means a series of well defined steps, which provides a procedure of calculations repeatedly successfully on the results of earlier steps. With the help of defined procedure the desired result can be obtained. F Highest Common Factor of the given positive integers. Ordinarily, if we want to find the HCF of two positive integers, we first find the Ch 10 Maths Class 10 Extra Questions Us factors of the two integers. For ex: For two integers 24 and 42, the common factors are 1, 2, Questions Ch Maths Extra 10 Class Us 10 3 and 6.
As 6 is the highest of other numbers, 6 is the HCF of 24 and Next the smaller integer is divided by the above remainder and the process is repeated till zero is obtained. The remainder in the last but one division is the required HCF. According to this theorem every positive integer is either a prime number or it can be expressed as the product of primes.
It is also known as Unique Factorization Theorem. Thus, any integer that is greater than 1 can be either a prime number or can be expressed ch 10 maths class 10 extra questions us a product of prime factors.
Note :. It is the only number that Ch 10 Maths Class 10 Extra Questions Us is both prime and. A chain of factors that is demonstrated in the form of a tree, is called a factor tree. HCF is the product of the smallest Ch 10 Maths Class 10 Extra Questions Us power of each common prime factor present in the numbers. The Ch 10 Maths Class 10 Extra QuestionsCh 10 Maths Class 10 Extra Questions Us Us product of the largest power of each prime factor present in the numbers is the LCM. Important Note:. We Ch 10 Maths Class 10 Extra Questions Us use the method of contradiction in order to prove irrationality of the numbers. If a prime number p divides a 2then p divides a, where a is a positive integer.
Let us understand how to write the decimal Ch 10 Maths Class 10 Extra Questions Us expansion of those rational numbers with terminating decimal expansion. The important questions for ch 10 maths class 10 extra questions us chapter is basically a compilation of higher and more advanced techniques a student can expect in Class 10 Ch 10 Maths Class 10 Extra Questions Us examinations. The questions of the chapter and the notes related to the ch 10 maths class 10 extra questions us provided by Vedantu will not only help you to understand the concept better but also solve the questions successfully.
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