# Numbers

We use numbers in our day to day life. They are often called numerals. Without numbers, we cannot do counting of things, date, time, money, etc. Sometimes these numbers are used for measurement and sometimes they are used for labelling.

The properties of numbers make them capable to perform mathematical operations on them.  These numbers are expressed in numeric forms and also in words. Also, they have varieties of types such as natural and whole numbers, odd and even numbers, rational and irrational numbers, etc. Apart from these, the numbers are used in various applications such as forming number series, maths tables, etc.

## Number Definition

A number is an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is known as numerals. A number system is a writing system for denoting numbers using digits or symbols in a logical manner. The numeral system

• Represents a useful set of numbers
• Reflects the arithmetic and algebraic structure of a number
• Provides standard representation

## Types of Numbers

The numbers can be classified into sets is known as the number system. The different types of numbers in maths are:

• Natural Numbers: Natural numbers are known as counting numbers that contain the positive integers from 1 to infinity. The set of natural numbers is denoted as “N” and it includes N = {1, 2, 3, 4, 5, ……….}

• Whole Numbers: Whole numbers are known as non-negative integers and it does not include any fractional or decimal part. It is denoted as “W” and the set of whole numbers includes W = {0,1, 2, 3, 4, 5, ……….}

• Integers: Integers are the set of all whole numbers but it includes a negative set of natural numbers also. “Z” represents integers and the set of integers are Z = { -3, -2, -1, 0, 1, 2, 3}

• Real Numbers: All the positive and negative integers, fractional and decimal numbers without imaginary numbers are called real numbers. It is represented by the symbol “R”.

• Rational Numbers: Any number that can be written as a ratio of one number over another number is written as rational numbers. This means that any number that can be written in the form of p/q. The symbol “Q” represents the rational number.

• Irrational Numbers: The number that cannot be expressed as the ratio of one over another is known as irrational numbers and it is represented by the symbol ”P”.

• Complex Numbers: The number that can be written in the form of a+bi where “a and b” are the real number and “i” is an imaginary number is known as complex numbers “C”.

• Imaginary Numbers: The imaginary numbers are the complex numbers that can be written in the form of the product of a real number and the imaginary unit “i”

## Numbers in Words

The list of numbers in words from 1 to 100 is given below: ## Number Series

In mathematics, the number series consists of a series of numbers in which the next term is obtained by adding or subtracting the constant term to the previous term. For example, consider the series 1, 3, 5, 7, 9, … In this series, the next term is obtained by adding the constant term “2” to the previous term. There are different types of number series namely,

• Perfect Square series
• Two-stage type series
• The odd man out series
• Perfect cube series
• Geometric series
• Mixed series

## Properties of Numbers

The properties of numbers are basically stated for real numbers in the number system. The common properties are:

### Commutative Property

If  a and b are two real numbers, then according to commutative property;

a+b = b+a

a.b = b.a

Example: 2+3 = 3+2

and 2 × 3 = 3 × 2

### Associative Property

If a, b and c are three real numbers, then according to associative property;

(a+b)+c = a+(b+c)

(a.b).c = a.(b.c)

Example: (1+2)+3 = 1+(2+3)

(1.2).3 = 1.(2.3)

### Distributive Property

If a, b and c are three real numbers, then according to distributive property;

a × (b + c) = a×b + a×c

Example: 2 × (3 + 4) = 2×3 + 2×4

2 × 7 = 6 + 8

14 = 14

### Closure Property

If a number is added to another number, then the result will be a number only, such as;

a+b = c; where a, b and c are three real numbers.

Example: 1+2 = 3

### Identity Property

If we add zero to a number or multiply by 1, the number will remain unchanged.

a+0=a

a.1 =a

Example: 5+0 = 5 and 5 x 1 = 5

If a number is added to its own negative number, then the result is zero.

a+(-a) = 0

Example: 3+(-3) = 3-3 = 0

### Multiplicative Inverse

If a number apart from 0, is multiplied to it’s own reciprocal then the result is 1.

a x (1/a) = 1

Example: 23 x (1/23) = 1

### Zero Product Property

If a.b = 0, then;

either a = 0 or b = 0.

Example: 7 x 0 = 0 or 0 x 6 = 6

### Reflexive Property

This property reflects the number itself.

a = a

Example: 9 = 9