A number is a mathematical concept used to quantify and represent quantities or values. It can be a whole number, fraction, decimal, or even an irrational number. Numbers have various properties and classifications, such as being prime or composite, positive or negative, real or imaginary. Understanding the concept of numbers is fundamental in mathematics and plays a crucial role in many fields of study.
Numbers are used to count different things or objects such as 1, 2, 3, 4 etc. They are often called numerals, without numbers, we can not do counting of things, date, money & time etc.
Table of Contents
What is Number System?
Number system is a system of reprocessing numbers in various ways. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
Types of Number System
There are four main types of number systems:
- Decimal Number System (Base- 10)
- Binary Number System (Base- 2)
- Octal Number System (Base- 8)
- Hexadecimal Number System (Base- 16)
What is Number?
A Number is an arithmetic value used to represent quantity. In other words, a number is a mathematical concept used to quantify or count. It can be an integer, fraction, decimal or even an imaginary and complex number.
Properties of Number
Closure Property : The sum or product of two number is also a number within the same set. e.g. 3+5=8, 2+3=5 etc.
Commutative Property : The order of addition or multiplication does not affect the result. e.g. ( 2+3)=(3+2) etc.
Associative Property : The way numbers are grouped in addition or multiplication does not change the result. e.g. 3+(4+5)=(3+4)+5
Distributive Property : Multiplication distributes over addition and subtraction. e.g. A(B+C)=AB+AC etc.
Identity Property : The sum of any number and zero is the number itself. e.g. 5+0=5, 0+7=7
Inverse Property : Every number has an additive inverse , such that adding a number to its inverse gives 0. e.g. [9+(-9)]= [9-9]=0
When we multiply to its multiplicative inverse gives 1. e.g. 4×1/4=1
All Types of Numbers
There are various types of numbers including:
Natural Numbers
Positive integers starting from 1. In other words, natural numbers are all positive integers from 1 to infinity, they are also called counting numbers. E.g. 1, 2, 3, 4, 5, ……… ∞
Whole Numbers
Non-negative integers including zero. In other words, whole numbers are any positive number that does not include fractional or decimal part. E.g. 0, 1, 2, 3, 4, …….. ∞
Integers
Positive and negative whole numbers along with zero. In other words, the collection of whole numbers and negative numbers together is called integers. E.g. ∞ ……-3, -2, -1, 0, 1, 2, 3, ……. ∞
Rational Numbers
Numbers that can be expressed as a fraction , where numerator and denominator are integers and denominator is not equals to zero. In other words, rational numbers are the numbers that can be written in the form of p/q, where p and q are integers and q is not equals to 0. E.g. 1, 0, -3/4, 5/7 etc.
Properties of Rational Numbers
- Rational numbers are like fractions, such as 1/2, or 4/5.
- They are made by dividing one whole number by another whole number.
- Every terminating and repeating decimal is a rational number.
Irrational Numbers
A irrational number is a real number that can not be expressed as a ratio of integers. In other words, numbers that have non- terminating and non-repeating decimal expansion. E.g. Π,√2,√3 etc.
Properties of Irrational Number
- An irrational number is non-terminating and non-repeating.
- An irrational number cannot be expressed as a fraction.
- The sum of a rational number and an irrational number is irrational.
Real numbers
All rational and irrational numbers combined. In other words, any number that we can think of , except complex numbers , is a real numbers. E.g. 1, 0, 4/6, Π,√2,√3 etc.
Complex numbers
Numbers in the form (a + bi), where “a” and “b” are real numbers and “i” is the imaginary unit. In other words, a complex number is an element of a number system that extends the real numbers with a specific element denoted “i” called the imaginary unit. e. g (3+5i) , and (2+7i) etc.
Apart from the above there exist other numbers namely
Even and odd numbers , Prime and composite numbers , Co-prime numbers, Twin prime numbers and Perfect numbers-
Even numbers
Numbers which are multiples of 2. In other words, Numbers which are divisible by 2. e.g. 2, 4, 6, 8, …….∞
Odd numbers
Numbers which are not multiples of 2. In other words, numbers which are not divisible by 2. e. g 1, 3, 5, 7, …… ∞
Prime Numbers
Numbers which have only 2 factor i.e. 1 and the number itself. In other words, a number that can only be divided by itself and 1 without remainders. e.g. 2, 3, 5, 7, 11, ……..∞
Composite Numbers
Numbers which have more than 2 factors. In other words, a number that can be divided by 3 or more numbers without remainders. e. g 4, 6, 8, 9, ……..∞
Co- prime Numbers
Two numbers having only one factor i.e.1 are called co- prime numbers. In other words, two integers are said to be co-prime , relatively prime and mutually prime if the only positive integer that is a divisor of both of them is 1. e.g. 6 and 49 are co-prime number.
Twin prime numbers
Two prime numbers whose difference is 2 are called twin prime numbers. In other words, a twin prime number is a prime number that is either 2 less or 2 more than another prime number. e.g. (3,5) and (11,13) etc.
Perfect Numbers
A perfect number is a number for which the sum of all its factors is equal to twice the number. In other words, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. E.g. 6, 28 496, 8128 etc.
Practice Questions
- What is Prime number?
- What is the difference between rational number and irrational number?
- What is number system? (simple definition)
Recommended Reading:
What is Irrational Number Class 9 (With Examples.)
Difference Between Place Value and Face Value- (With 10 Solved Example).
FAQs
Q.1 what is the smallest prime number?
Answer -2
Q.2 What is the largest natural number?
Answer- can not determined.
Q.3 What is Irrational Numbers?
Answer- A number is called an irrational number if it cannot represent in the form of ratio.
Q.4 What is Real Numbers?
Answer- All rational and irrational numbers together called real numbers.