In this chapter, students explore important properties of real numbers, focusing mainly on integers and their factorisation. The chapter begins with Euclid’s Division Algorithm, which helps in understanding divisibility and finding the HCF of numbers.
Students then learn the Fundamental Theorem of Arithmetic, which states that every composite number can be expressed as a unique product of prime numbers. Using this theorem, they learn how to find HCF and LCM through prime factorisation.
The chapter also introduces proofs of irrational numbers such as √2, √3, and √5, and explains how to determine whether a rational number has a terminating or non-terminating repeating decimal expansion.
