SOLUTION: Find the Fraction form for each repeating decimal 0.010101.....

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Question 71382: Find the Fraction form for each repeating decimal 0.010101.....
Found 2 solutions by checkley75, jim_thompson5910:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
1/99=.0101010101

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
let x=0.010101. Now multiply x by 100 so the decimal moves two places to the right. So 100x=1.010101, if you notice theres a similarity of .010101 between each term which can be canceled out by subtraction
                  100x=1.010101
                   - x=0.010101      
                ----------------                                           
                   99x=1

Now just solve for x
99x=1
x=1%2F99
Hope that all makes sense. You can always check this by calculating 1/99 to get .010101.