Recurring decimal tricks

Here are few tricks for Recurring decimals...........


Recurrence can be defined as reoccurrence of same thing.
to solve recurring decimals problems,we need to follow few basics.

Trick 1:(0.ab....)

Let N be a number with 'n' digits in it ,
and M be another 'n' digit number which has all 9's
then  N/M produces a number 0.NNNNNNNNN....................

e.x: 12/99=0.1212........
e.x:1234/99999=0.12341234..........
e.x: 8567/9999=0.85678567........


Trick 2:(0.abbb...........)

 0.abbbbbbbb.........  is equivalent to (ab-a)/90


recurrence


 Generic Trick:
You can create your own tricks for any recurring decimal using these steps,
conversion of recurring decimal to fraction:
steps:

  1. Let x equal the repeating decimal you are trying to convert to a fraction
  2. Examine the repeating decimal to find the repeating digits.
  3. Multiply with 10's to get 2 equations where you get only recurring digits on fractional part.
  4. Solve two equations to get the fraction.
**********************************************************************************************************************************Example 1:

x=0.555555..........     (EQN 1)
recurring decimal is 5

Move decimal towards right:
10x=5.555555.................   (EQN 2)

Now solve EQN 1,2
10x-x=5.55555................-0.555555...............
=> 9x=5
=>x=5/9


Example 2:

x=1.04242..........
recurring decimal is 42

Move decimal towards right
10x= 10.4242...............     (EQN 1)
1000x = 1042.4242..............     (EQN 2)


Now solve EQN 1,2
1000x-10x=1042.4242..........-10.4242.........
990x=1032
x=1032/990



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