Number System: Introduction

This chapter is the most important chapter in the Quantitative Aptitude section.The students are advised to prepare each topic of this chapter, topics of this chapter will help you to solve the questions of other chapters of quantitative aptitude too.
In this chapter, in every topic, definition is given with example, it makes the topic easy to understand.

Number: A number is an arithmetic value expressed by a symbol or figure to represent a perticular quantity and used for counting, measuring and calculation.

Number System: Number system is a way for representing the numbers as natural numbers, whole numbers, odd numbers, even numbers, rational numbers, irrational numbers etc.

Types of Numbers: Some important types of numbers are given below-

Natural Numbers: The numbers generally used to count something are known as Natural Numbers.It include numbers from 1 to 9. Zero (0) is not a natural number. Example: {1, 2, 3, 4, 5, 6, 7, 8, 9.........}.

Whole Numbers: The natural numbers including zero (0) are known as Whole Numbers. Example: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9.........}

Even Numbers: The numbers which are divisible by 2 are known as Even Numbers. Example: {2, 4, 6, 8, 10, 12, 14.........}

Odd Numbers: The numbers which are not divisible by 2 are known as Odd Numbers. Example: {1, 3, 5, 7, 9, 11, 13,.........}

Integer Numbers: The natural numbers with their negative numbers including zero (0) are known as Integer numbers. Example: {.........-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.........}

In the above example of integer numbers, left side numbers which are negative are knwon as Negative Integer numbers and right side numbers which are positive are knwon as positive Integer numbers. One important point is that the number Zero (0), which is neither positive integer number nor negative integer number.

Prime Numbers: The numbers which are divisible by 1 and itself only are known as Prime Numbers. The number 2 is the only Even prime number and all other prime numbers are odd. Example: {2, 3, 5, 7, 11, 13, 17.........}

Composite Numbers: All natural numbers, which are greater than 1, but not the prime numbers are known as composite numbers. Example: {4, 6, 8, 9, 10, 12, 14, 15,.........}

Rational Numbers: Any number which is in the form of fraction (a/b) of two integers is called rational number, where denomenator b must be equal to or greater than 1, it can not be zero.and note that every integer number is a rational number too. Example: {\(\frac{1}{2}, \frac{2}{3}, \frac{5}{8}, \frac{6}{9}, -1, -2.........\)}

Irrational Numbers: Any number which can not be in the form of fraction (a/b) for any integers is called irrational number. Example: {\(\pi\), \(\sqrt 2\), \(e\), \(\phi\),.........}

Real Numbers: All the rational and irrational numbers are called real numbers. Example: {\(\frac{1}{2}, \pi, \frac{2}{3}, \sqrt 2, \frac{5}{8}, \frac{6}{9}.........\)}