Number System in Maths: Basic to Advance Formulae & Tricks
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| Number System in Maths |
- What is Number System in Maths?
- Find the face value of digits 4, 3 and 5 in numeral 98430421?
- Find the place value of digits 4, 3 and 2 in numeral 9843021?
- Types of Number System
- Natural Numbers
- Whole Numbers
- Integers
- Even Numbers
- Odd Numbers
- Prime Numbers
- Real Numbers
- Rational Numbers
- Irrational Numbers
- Co-primes Numbers
- Representing numbers on number lines
- Divisibility Rules in Number System
Number System is one of the most important chapter in maths. It plays a vital role in quantitative aptitude. We often heard that mathematics is the most lengthy and tough subject, this is why? 'Bcoz lack of basic formula and proper concept of Number system'. Number system is the base of quantitative aptitude.
To crack any exams like (Bank, SSC, Railway etc) a candidate must have understanding of this chapter at finger tips.
I hope after reading this post you become master in Number Systems in Maths by understanding basic to advance formulae its uses and tricks to solve all types of questions asking from this chapter.
What is Number System in Maths?
In short a number system is a system representing different types of numbers, their study, relationship and rules. A number is a mathematical value used for counting and measuring various types of objects and for performing arithmetic calculations. It is a combination of digits and a digit is a set of 10 symbols ranging from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
What is Face Value and Place Value of the Digits in Number System?
Face Value
In a numeral the face value of any number can be represented by the value of the digit itself irrespective of its place in the numeral.
For Example:
Find the face value of digits 4, 3 and 5 in numeral 98430421?
In the numeral 98430421-
- the face value of 4 is 4
- the face value of 3 is 3
- the face value of 5 is 5
Place Value
In a numeral the place value of a number represents the position of the digit and changes according to the change of its place.
For Example:
Find the place value of digits 4, 3 and 2 in numeral 9843021?
In the numeral 9843021-
- the place value of 4 is 4X10000 = 40000
- the place value of 3 is 3X1000 = 3000
- the place value of 2 is 2X100 = 200
Types of Number System:
Their are various types of number system in maths-
- Natural Numbers
- Whole Numbers
- Integers
- Even Numbers
- Odd Numbers
- Prime Numbers
- Real Numbers
- Composite Numbers
- Co-Primes Numbers
1. Natural Numbers
All counting numbers are Natural Numbers. They are denoted by N.
For Example: N = {1,2,3,4,5.................}
- All natural numbers are positive
- Zero is not a natural number
- The smallest natural number is 1
- Largest natural number is ∞
2. Whole Numbers
- The smallest whole number is zero
- The Largest whole number is ∞
- Whole numbers are also called as non-negative integers
3. Integers
- The smallest integer is zero -∞
- The Largest integer is ∞
- 0 is neither positive nor negative 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, ..........etc.
The unit's place of every odd number will be 1, 3, 5, 7 or 9.
6. Prime Numbers
A number greater than 1 having exactly two factors namely 1 and itself is called a prime number.
For Example: 2, 3, 5, 7, 11, 13, .......etc
- 2 is the only even prime number
- A prime number is always greater than 1
- 1 is not a prime number
- There are 25 prime numbers between 1 to 100
- There are 15 prime numbers between 1 to 50
7. Real Numbers
Real numbers is a set of rational numbers like positive and negative integers, fractions, and irrational numbers. The set of real numbers is denoted by R.
For Example: 7/9, 
3, 7, 
, 8/9, 0.333, 0.7 etc
There are two types of Real Numbers
a) Rational Numbers
b) Irrational Numbers
a) Rational Numbers
A number that can be expressed in the form of p/q is called a rational number, where p and q are integers and q 
0.
For Example: 2/5, 7/9, -1/9, 13/15, 6 etc
The decimal form of rational number is either terminating or non-terminating.
Terminating (or finite decimal):
A terminating decimal is a decimal number with a finite number of digits after the decimal point.
For Example: 17/4= 4.25, 21/5=4.2 etc
Non-Terminating (or recurring decimal):
A non-terminating decimal will never end but may predictably repeat one or more values after the decimal point
For Example: 16/3= 5.333..., 2/3= 0.666... etc
b) 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: 2, 3, 7, etc.
- π is an irrational number as 22/7 is not the actual value of π but it is its nearest value
- Non-periodic infinite decimal fractions are called as irrational number
8. Composite Numbers
A number greater than 1 which are not prime are called composite numbers. They must have atleast one factor apart from 1 and itself.
For Example: 4, 6, 8, 9,10, 12 etc.
- 1 is neither a prime number nor composite number
- Composite numbers can be both odd and even
- 4 is the smallest composite number
9. Co-primes Numbers
Two natural numbers are said to be co-primes, if their HCF is 1.
For Example: (7, 9),(4, 5) etc
- Co-prime numbers may or may not be prime
Representing numbers on number lines
Divisibility Rules in Number System
Divisible by 2: If the last 1 digit contains 0,2,4,6 and 8.
Divisible by 3: If the sum of its digits is divisible by 3.
Divisible by 4: If the last two digits is divisible by 4.
Divisible by 5: If the last digits ends with 0 or 5.
Divisible by 6: If the number divide by 2 and 3 both.
Divisible by 8: If the last three digits is divisible by 8.
Divisible by 9: If the sum of its digits is divisible by 9.
Divisible by 10: If the last digit ends with zero.
Divisible by 11: (Sum of its digit in odd places - Sum of its digits in even places)= 0 or multiple of 11
For Example: Is the number 2345678 divisible by 11?
2+4+6+8 = 20
3+5+7 = 15
then subtract 20-15 = 5 (If this difference is 0 or multiple of 11 then the number is divisible by 11 otherwise not)