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. Afterward, the types of the 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, the 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
Irrationals and Reals
- Irrational Numbers
- Square Root of Two is Irrational
- Decimal Representation of Irrationals
- Exactness of Decimal Representations
- The Rational Line has Irrational Holes
- Real Numbers and Real Line
- Complex Numbers - Points in the Plane