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Natural Numbers : Numbers which are used for counting the objects are called
natural numbers. They are denoted by N.
N = { 1, 2, 3………………..}
All positive integers are natural numbers.
Whole numbers :- When ‘zero’ is included in the natural numbers, they are known as
whole numbers.
They are denoted by W.
W= { 0, 1, 2, 3……………….}
Integers : All natural numbers, zero and negatives of natural numbers are called as
integers.
They are denoted by I.
I = { ………………..,-3, -2, -1, 0, 1 , 2, 3………………}
Rational numbers : The numbers which can be expressed in the form of
are integers and
are called rational numbers
where P and Q
They are called by Q.
Irrational numbers : The numbers which cannot be written in the form of
Q are integers and
are called irrational numbers.
where P and
When these numbers are expressed in decimal form, they are neither terminating nor
repeating.
Number System
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Real numbers : Real numbers include both rational as well as irrational numbers.
Positive or negative, large or small, whole numbers or decimal numbers are all real
numbers.
e.g.= 1, 13.79, -0.01,
etc.
Imaginary numbers : An imaginary number is a complex number that can be written as a
real number multiplied by the imaginary unit ‘i’ which is defined by its properly
Note : Zero (0) is considered to be both real and imaginary number.
Prime number : A prime number is a natural number greater than 1 and is divisible only
by 1 and itself.
e.g.2, 3, 5, 7, 11, 13, 17 ,19 ………….etc.
Note :- 2 is the only even prime number.
Composite Numbers : A number, other than 1, which is not a prime number is called a
composite number .
E.g. 4, 6, 8, 9, 10, 12, 14, 15 ……….etc.
Note :1 1 is neither a prime number nor a composite number.
2 there are 25 prime numbers between 1 and 100.
To find whether a number is prime or notTo check whether the number is prime or not,
1 We take an integer larger than the square root of the number. Let the number be ‘k’.
2 Test the divisibility of the given number by every prime number less than ‘k’.
3 If it is not divisible by any of them, then the given number is prime otherwise it is a
composite number.
E.g.= Is 881 a prime number ?
Sol- The appropriate square root of 881 is 30.
Number System
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Prime number less than 30 are 2, 3, 5, 7, 11, 13, 17,19, 23,29.
881 is not divisible by any of the above numbers, so it is a prime minister.
Co-prime numbers : Two numbers are co-prime of their HCF is 1.
E.g. (2,3), (3,4) , (5,7), (3,13) etc.
Even numbers : The number which is divisible by 2 is called even number.
E.g. – 2, 4, 6, 8…………….
Odd numbers – The number which is not divisible by 2 is called odd number.
e.g.= 3, 5, 7, 9…………..
Consecutive numbers : A series of numbers in which the succeeding number is greater
then the preceding number by 1 is called a series of consecutive numbers.
i.e., Difference between two consecutive numbers is 1.
Some Rules on Counting Numbers
1. Sum of all the first n natural numbers
Q. Find the sum of first 20 natural numbers.
Ans- Sum of 1 to 20
Q. Find the sum of numbers from 11 to 20.
Number System
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2. Sum of first n old numbers =
Q. What is the sum of first 10 odd numbers ?
Ans- Sum of first 10 odd numbers =
Q. Find the sum of 9+11+13+………+29
Ans – 1+3+5+…………+29=
(as there are 15 odd numbers from 1 to 29)
1+3+5+7=
9+11+13+29=225-16=209
3. Sum of first n even numbers
Q. What is the sum of even numbers between 1 and 50 ?
Q. Find the value of 12+14+……….+30.
Ans- (2+4+6+…….+30) has 15 even numbers
Number System
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