Number System 1|Theory|number basics,recurring decimals

meette 2/23/2015 11:35:00 am , , No comments
This is the very first post so I am super excited. I'll start with the absolute basics of number system and go into details of every topic. Then I will be posting overwhelming no of problems for you guys to solve.. Happy Learning :)

Classification of numbers.

number classification


So numbers are broadly classified into real numbers and imaginary numbers.
Real numbers are those numbers which can be expressed in the number line whereas imaginary numbers are those which cannot be expressed in the number line. They don't exist in real life. For e.g. can a number like √-3 exist  in real life?No

Now real numbers are further subdivided into rational and irrational numbers.

Rational numbers are those which can be expressed in the form p/q where p is the numerator and q is the denominator and q cannot be 0. All integers positive or negative or zero are rational numbers

is .777777.... a rational number? yes as it can be expressed as 7/9.
So recurring decimals are rational numbers. So are all proper and improper fractions like 4/9,2/3,8/7 etc.

Irrational numbers are those which cannot be expressed in the p/q form. Eg √2 ,√3

What about the number ∏? 
when expressed in the decimal form it is 3.141592... and is non terminating hence irrational however we express ∏ as 22/7 which is rational. The thing we need to remember is that 22/7 is only a approximate value of ∏.

Integers- {....-3,-2,-1,0,1,2,3,4....}
Natural numbers-{1,2,3,4…}
Whole numbers-{0,1,2,3,...} So whole numbers are natural numbers plus zero. Both whole numbers and natural numbers are subset of integers.


Finding the fraction form of a recurring decimal:


1.What is the fraction form of .3333… ?
Ans: let A=.3333…  then
        10xA=3.3333…
                 =3+.33333=3+A
Thus rearranging 9A=3 or A=3/9

2.What is the fraction form of .363636… , .324324324…. ?
Ans: They are 36/99 and 324/999 .So the number of 9 is same as the no of recurring digits.

2.What is the fraction form of 2.42363636… ?
Ans : let A=2.42363636… then
          100xA=242.363636..     -à(1)
           10000xA=24236.3636…     -à(2)
Subtraction (1) from (2) we get 9900A=23994 So A is 23994/9900

So the general formula for ab.cde̅f̅g̅  is (abcdefg-abcd)/99900


The concept of recurring decimal can be tested and I will be posting problems for you to solve and share the links here. 

 Solve the problems given in the followin link(s)
http://www.jotoshob.blogspot.in/2015/02/number-systemproblem-set-1number.html

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