SOLUTION: Write the repeating decimal 0.7575 . . . as a fraction

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Question 295806: Write the repeating decimal 0.7575 . . . as a fraction
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=0.7575 where the '75's continue on forever


Multiply both sides by 100 to get 100x=75.7575 where the '75's continue on forever


From here, subtract both sides by 'x' to get 100x-x=75.7575-x. Now plug in x=0.7575 on the right side to get 100x-x=75.7575-0.7575


Now combine like terms: 99x=75 and then divide both sides by 99 to get x=75%2F99


Because we made x=0.7575 and we found that x=75%2F99 as well, we can say that 75%2F99=0.7575 (where the 75's go on forever). Note: you can use your calculator to confirm.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
25/33
http://mathforum.org/library/drmath/view/57041.html