# Number System

## Concept Learning Sessions

Session # 1 Introduction to Number System. In this session utility of numbers (Natural, Whole and Integers only), types of numbers, limitations of Sets of various types of numbers has been discussed. Closure property and concept of number line has also been discussed.

Session # 2 Definition of Rational Numbers. In this session, definition of rational numbers has been discussed. Why are rational numbers called so and criteria of rationality has also been discussed.

Session # 3 How to represent rational numbers on a number line. After this video Problem Session # 1 should be covered.

Session # 4 How to find out rational numbers between two Given rational numbers. Explanation and solved examples

Session # 5 Decimal representation of rational numbers. Terminating and Non-terminating-recurring decimal representation

Session # 6 Decimal Representation of Fractions with denominators only with powers of 2 and 5

Session # 7 Conversion of Decimal Numbers (terminating) into Rational Numbers of the form p/q. Example: 0.645

Session # 8 Conversion of Decimal Numbers (non-terminating-recurring, pure form) into Rational Numbers of the form p/q. Example: 0.33333333.....

Session # 9 Conversion of Decimal Numbers (non-terminating-recurring, mixed form) into Rational Numbers of the form p/q. Example 0.3521212121.....

Session # 10 What are Irrational Numbers? Why are they called so?

Session # 11 Prove that √2 is an irrational number

Session # 12 Some results on irrational numbers

Session # 13 Finding irrational numbers between two given numbers

Session # 14 Proving a given number (√3 - √2) is an irrational number

Session # 15 Plotting an irrational number (√2) on a number line.

Session # 16 How to plot a √x (for any Real x) on a number line using Geometry. The process has been explained using an example of √7.4

## Problem Solving Sessions

Session # 1 Problem on representing a rational number on a number line