SOLUTION: Use the infinite geometric sum formula to write 0.757575... as a fraction in reduced form. Show all steps neatly.

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Question 1066079: Use the infinite geometric sum formula to write 0.757575... as a fraction in reduced form. Show all steps neatly.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
If |r| < 1 then +sum%28a%2Ar%5En%29++=+a%2F%281-r%29+
We have a=75/100
r = 1/100

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Answer is highlight%2875%2F99%29
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Check: One way is to just divide 75/99 to see it gives you 0.75757575…
Another way is as follows (this works on any decimal that repeats):
Let n = 0.75757575….
100n = 75.757575...
Subtract top from bottom (all numbers to the right of decimal cancel):
99n = 75 —> n=75/99