The Chapter provides you glimpse into the world of real numbers, introducing you to the concepts like Euclid’s Division Lemma, Euclid’s algorithm.
The chapter also opens up fundamental property of arithmetics, which states:
Theorem 1.2 (Fundamental Theorem of Arithmetic) : Every composite number can be expressed ( factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Then it helps your factorize composite numbers to help you obtain HCF and LCM of a number.
Thereafter, it explains the concepts of irrational number.
Overall, this chapter helps you understand some basic concepts of mathematics, which, to an extent you may have learnt in previous classes but in a different way and with a twist.
Here are the Key Concepts:
- An algorithm is a series of well defined steps which gives a procedure for solving a type of problem.
- A lemma is a proven statement used for proving another statement.
- Euclid’s division algorithm is a technique to compute the Highest Common Factor
(HCF) of two given positive integers. - Two numbers a and b (a > b) can be represented as a = bq+r where q and r are real numbers
- If r = 0; a is a factor of b
- This method can be used to calculate HCF of two numbers a and b
- The same lemma can be used to denote many properties of real numbers
- Fundamental theory of arithmetics is defined above
- HCF (a,b) x LCM (a,b) = a xb
- Fundamental theory of arithmetics can be used to prove irrationality of a number
Here, we are including a small quiz relating to this chapter and then lets you register for whole question set.
The Question set has been designed in the format of board exam paper, giving you enough practice to prepare you for the final exams and ensuring you earn all the concepts required to solve any question that the exam paper may throw onto you, relating to this chapter.