Converting Decimals to Fraction I know how to convert most rational decimal but I am having trouble to convert 1.8768686868... or        0.95287928792879... 
I did end up solving one of these tricky decimals problems but I was wondering if there is a quick simple technique for this?
 A: $$1.87\overline{68} = \dfrac{187}{100} + \dfrac{1}{100} \dfrac{68}{100-1} = \dfrac{18581}{9900}$$
A: Let $x = 1.8768686868...….$ eqn (1)
The repetition starts from $2$ decimal places. This means we need to multiply (1) by $10^2$ and get
$100x = 187.686868……$ eqn (2)
To cancel the $.686868…$ we need another supporting equation:-
$10000x = 18768.686868….$ eqn(3)
Do (3) – (2) and solve for x.
A: $ \text{ Repetition part starts in the thousandths spot and ends in the 10 thousandths spot.  Let } x=1.876868686868.... \text{ then } 10,000x=18768.686868686868.... \text{ Now find the difference } 10,000x-x=18768.68686868...-1.8768686868....=18768.68-1.87 \\ 9,999x=18766.81 \\ \text{ Now multiply both sides by 100: } 999900x=1876681 \text{ now you can solve for } x $ 
A: Count the length of the repeating part.  In your first example it is two digits.  Multiply by $10$ to that power and subtract.  So for your first example, let $x=1.87686868\dots $  Then $10^2x=100x=187.686868\dots $  That gives $99x=187.686868\dots - 1.87686868\dots =185.79$  The point of counting the repeat is to get the infinite tail to subtract to nothing.
