Numbers and Number System

This chapter starts with a basic overview of natural and whole numbers along with integers. It then proceeds to describe the theory of rational numbers. Next, rational numbers are described in the context of a number line, and an interesting thought experiment is presented to show that between any two rational numbers, no matter how close, there will exist infinitely many rational numbers. Afterwards, the types of decimal representation of rational numbers (terminating and non-terminating) are explained. Following this, it is observed that there are discontinuities along a rational number line and irrational numbers are introduced to explain this observation. Further, decimal representation of irrational numbers is taken up for explanation, which is followed by an introduction of complex numbers. Finally, rationalization of irrational expressions is explained, supplemented by a section on using algebraic identities.

In addition to preparing for the JEE mains and advanced exams, Cuemath Founder Manan Khurma's study material is helpful for students who are appearing for CBSE, ICSE and other State board exams.

From Naturals to Rationals

• Natural Numbers
• Whole Numbers
• Integers
• Rationals
• The Rational Line
• The Zooming Thought Experiment
• Decimal Representation of Rational Numbers
• Discontinuity of the Rational Line

Irrationals and Reals

• Irrational Numbers
• Irrationality of √2
• Decimal Representation of Irrationals
• Exactness of Decimal Representations
• The Rational Line has Irrational Holes
• Reals and the Continuous Real Line
• Numbers beyond the Real Set
• Complex Numbers - Points in the Plane
• What is IOTA?

Working with Irrational Expressions

• Surds
• Conjugates and Rationalization
• Rationalization in Irrational Expressions
• Using Algebraic Identities