Number Systems : Number Systems INTRODUCTION
By Malay
What will we learn today? : What will we learn today? Number Line
Types of number
Finding rational numbers between two whole number
Trick of the session
Number Line : Number Line Negative numbers Positive numbers
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…-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 ...
Types of number : Types of number Natural Number : Denoted by N
Generally the numbers we count are called natural numbers(N).
Example : 1,2,3,4 ….
Whole Number : Denoted by W
Put one more number i.e. 0(Zero) together with natural number and it forms whole number.
Example : 0,1,2,3,4 ….
Integers : Denoted by Z
Put all the negative numbers along with whole numbers and it forms Integers.
Example : …-4,-3,-2,-1,0,1,2,3,4….
Types of number contd… : Types of number contd… Rational Numbers : Denoted by Q
A number which can be represented as p/q where q is not equal to 0(zero) is called as rational number.
Irrational Numbers : Denoted by Q’
We will be discussing about this type of numbers in the next class. Q N Z W
Find rational numbers between two whole numbers : Find rational numbers between two whole numbers Method 1
If a and b are two numbers then a number c can be found in between these two numbers and c = (a+b)/2
Method 2
If a,b are two numbers and we have to find k numbers in between these two numbers then represent a and b as rational number with k+1 as denominator. Then keep on increasing the numerator by 1.
Example : Example Q : Find four numbers between 5 and 6.
Solution by method 1
1st number between 5,6 = (5+6)/2 = 11/2
2nd number between 5 and 11/2 = (5+11/2)/2 = 21/4
3rd number between 6 and 11/2 = (6+11/2)/2 = 23/4
4th number between 5 and 21/4 = (5+21/4)/2 = 41/8
Solution by method 2
We have to find 4 numbers between 5 and 6. So represent 5 and 6 as rational number with denominator 5(4+1).
5 = 25/5, 6=30/5
To find 4 numbers keep increasing numerator by 1 i.e.
26/5, 27/5, 28/5 and 29/5.
Trick of the session : Trick of the session Finding square root of a number ending with 25.
For last two numbers put a 5 and represent other part of the number as k*(k+1) and the square root is k5.
Example : find square root of 2025
2025
4*5
4 5
So square root of 2025 is 25.
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