Number System:
A system in which we study different types of numbers, their
relationship and rules govern in them is called as number
system.
In the Hindu-Arabic system, we use the symbols 0, 1, 2, 3, 4, 5,
6, 7, 8 and 9. These symbols are called digits. Out of these ten
digits, 0 is called an insignificant digit whereas the others are
called significant digits.
Numerals
A mathematical symbol representing a number in a systematic manner is called a numeral represented by a set of digits.
How to Write a Number
To write a number, we put digits from right to left at the places
designated as units, tens, hundreds, thousands, ten thousands,
lakhs, ten lakhs, crores, ten crores.
Let us see how the number 308761436 is denoted
It is read as
Face Value and Place Value of the Digits in a Number
Face Value
In a numeral, the face value of a digit is the value of the digit itself irrespective of its place in
the numeral. For example In the numeral 486729, the face value of 8 is 8, the face value of 7 is
7, the face value of 6 is 6, the face value of 4 is 4, and so on.
Place Value (or Local Value)
In a numeral, the place value of a digit changes according to the change of its place.
Look at the following to get the idea of place value of digits in 72843016.
It is clear from the above presentation that to obtain the place value of a digit in a numeral, we multiply the
digit with the value of its place in the given numeral.
Types of Numbers
1. Natural Numbers
Natural numbers are counting numbers. They are denoted by N. For example N = {1,2,3,…}.
♦ All natural numbers are positive.
♦ Zero is not a natural number. Therefore, 1 is the smallest natural number.
2. Whole Numbers
All natural numbers and zero form the set of whole numbers. Whole numbers are
denoted by W.
For example W = {0,1,2,3,…}
♦ Zero is the smallest whole number.
Whole numbers are also called as non-negative integers.
3. Integers
Whole numbers and negative numbers form the set of integers. They are denoted by/.
For example / = {…,-4,-3,-2,-1,0,1,2,3,4,…}
Integers are of two types. (i) Positive Integers Natural numbers are called as positive integers. They are
denoted by I .
For example I
+ = {1,2,3,4,…}
(ii) Negative Integers Negative of natural numbers are called as negative integers. They are denoted by
I~. For example I~ ={-1,-2,-3,-4,…}
♦ ‘0’ is neither +ve nor -ve integer.
4. Even Numbers
A counting number which is divisible by 2, is called an even number. For example 2, 4, 6, 8, 10, 12, … etc
The unit’s place of every even number will be 0, 2, 4, 6 or 8.
5. Odd Numbers
A counting number which is not divisible by 2, is known as an odd number.
For example 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, … etc. ♦ The unit’s place of every odd number will be 1, 3, 5,
7 or 9.
6. Prime Numbers
A counting number is called a prime number when it is exactly divisible by, 1 and itself.
For example 2, 3, 5, 7, 11, 13, … etc.
♦ 2 is the only even number which is prime
♦ A prime number is always greater than 1.
♦ 1 is not a prime number. Therefore, the lowest odd prime number is 3.
♦ Every prime number greater than 3 can be represented by 6n + 1, where n is integer
7. Composite Numbers
Composite numbers are non-prime natural numbers. They must have atleast one factor apart from 1 and
itself
For example 4, 6, 8, 9, etc.
♦ Composite numbers can be both odd and even.
♦ 1 is neither a prime number nor composite number.
8. Coprime
Two natural numbers are said to be coprimes, if their HCF is 1. For example (7, 9), (15, 16)
♦ Coprime numbers may or may not be prime
9. Rational Numbers
A number that can be expressed as p/q is called a rational number, where p and q are inteqers and a ■*■ 0.
10. Irrational Numbers
The numbers that cannot be expressed in the form of p/q are called irrational numbers, where p and q are
integers and q * 0.
For example -J2, V3, -Jl, VTT etc.
♦ 7C is an irrational number as 22 / 7 is not the actual value of ∏ but it is its nearest value.
♦ Non-periodic infinite decimal fractions are called as irrational number.
11. Real Numbers
Real numbers include rational and irrational numbers both,
♦ Real numbers are denoted by R.
Basic math is nothing but the simple or basic concept related with mathematics. Generally, counting, addition, subtraction, multiplication and division are called the basic math operation. The other mathematical concept are built on top of the above 4 operations
