0NUMBER SYSTEM
Digits : - The symbol 0,1,2,3,4,5,6,7,8,9 are called digit. Digits are used to represent any number. The number 0 is called insignificant digit while other ( 1,2,3,4,5,6,7,8,9) are called significant digit.
Numerals :- A group of digit representing a number is called numerals. There are two way to represent a number (i) Indian Number system (ii) International number system.
To write a number we put digit from right to left at the place designated in the number system.
Indian Number System
Example : - 58,21,77,548 ( write and read this number according to Indian Number System )
| Ten Crore | Crore | Ten | Lakh | Ten Thousand | Thousand | Hundred | Ten | Unit |
| 5 | 8 | 2 | 1 | 7 | 7 | 5 | 4 | 8 |
It is read as “Fifty Eight Crore Twenty one lakh Seventy Seven thousand Five hundred forty Eight”.
Similarly,
International Number System
| Billion | Hundred million | Ten Million | Million | Hundred Thousand | Ten Thousand | Thousand | Hundred | Ten | Ones |
| 5 | 8 | 2 | 1 | 7 | 7 | 5 | 4 | 8 | 3 |
It is read as “ Five Billion Eight Hundred Twenty One Million Seven Hundred Seventy Five Thousand Four Hundred Eighty Three”.
Value of Numerals
- Face Value :- Face value of a digit is the value of the digit itself irrespective of its place in the numerals. Example : - 41232 → The Face value of 3 is 3 while the face value of 4 is 4.
- Place Value : - The Place value of a digit is the place at which digit is present in the numerals. Example :- 41232 → The digit 3 is in tenth place of numerals so the place value of 3 is 30 while the digit 4 place in tenth thousand place in numerals so the place value of 4 is 40,000.
Classification of Numbers
Natural Numbers :- All counting number except 0 are called natural numbers. It is denoted by ‘N’. Example :- 1,2,3,4,5,6,7,…………… etc.
Whole Numbers :- All naturals number along with 0 are called whole numbers. It is denoted by ‘W’. Example :- 0,1,2,3,4,…. etc.
Even Number :- All Counting number which is divisible by 2 are called even number. E.g. 2,4,6,8,10, …….. etc.
Odd Number :- All counting number which are not divisible by 2 are called odd number. E.g. 1,3,5,7,11, …….. etc.
Prime Number :- A number is called prime number if the number have only two factors. The one factor is the number itself and other factor is 1. E.g. 3,5,7,11,13, ….etc.
Co-Prime Number :- Two natural number are said to be co-prime number if their highest common factor is 1. Co-Prime number are also called relatively prime number. E.g. (9,2), (5,6), (11,13) etc.
Composite Number :- A number is said to be composite number if their factors are other than 1 and itself i.e. composite number have more than two factors
Integer :- The collection of all whole number along with the negative number are called composite number. The set of integer is denoted by Z or I. e.g. -4,-2,0,2,4,6 ……..etc. Here -4, -2 are called negative integer while 2,4,6 etc. are positive integer.
Rational Number :- A number which can be expressed in the form of p/q where p and q are integer and q ≠ 0 are called rational number. E.g. 3/7, 5/9,8,3 etc.
Irrational Number :- A number which can not be expressed in the form of p/q , wher p and q are integer and q ≠ 0 are called irrational number. E.g. √2,√3 etc.
Real Number : All rational and irrational number are called real number. E.g. 7/5, √2, 9,8, π ...etc.
