Rational and Irrational NumbersBoth rational and irrational numbers are real numbers. This Venn Diagram shows the relationships between sets of numbers. Notice that rational and irrational numbers are contained in the large blue rectangle representing t…

Table of Properties of Real NumbersLet a, b, and c be real numbers, variables, or algebraic expressions. (These are properties you need to know.)

PRIME FACTORISATIONPrime factorisation is the process by which a composite number is rewritten as the product of prime factors. Example 1: Find out the prime factorisation of 30. First we will see whether the given number is divisible by a least prime nu…

Fundamental Theorem of ArithmeticWe have discussed about Euclid Division Algorithm in the previous post.Fundamental Theorem of Arithmetic: Statement: Every composite number can be decomposed as a product prime numbers in a unique way, except for the orde…

Find The HCF And LCM using Prime Factorisation MethodRelation between two numbers and their HCF and LCM Consider two numbers 18 and 24. Prime factorisation of 18 = 2 × 3 × 3 Prime factorisation of 24 = 2 × 2 × 2 × 3 So, HCF = 2 × 3 = 6 LCM = 2 × 2 × 2 × …

What Is Irrational NumberA number is irrational if and only if its decimal representation is non-terminating and non-repeating. e.g.√2, √3, π ……………. etc. Rational number and irrational number taken together form the set of real numbers.If a and b are t…