SOLUTION: What fraction is represented by 0.17952? where the 952 is repeating.

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Question 833306: What fraction is represented by 0.17952? where the 952 is repeating.
Found 3 solutions by Alan3354, KMST, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What fraction is represented by 0.17952? where the 952 is repeating.
-------------------
Ignore the 17 for now
-------------
n = 0.952952952...
1000n=952.952952...
- 1n =-00.952952...
----------------------- Add
999n = 952
n = 952/999
==================
--> 17 + 952/999


Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
So 17.952952952.... =17%26952%2F990
Similarly,if x=0.17952952952%22...%22
1000x=179.52952952952%22...%22
Then,
1000x-x=179.52-0.17 (the rest of the digits cancel out)
999x=179.35
99900x=17935
x=17935%2F99900
Can we simplify that fraction?

17935 is not divisible by 2 or by 3 , but we can divide it by 5
17935%2F5=3587 and 99900%2F5=19980 so
17935%2F99900=3587%2F19980
3587 is not divisible by 5 or 37 so we cannot simplify the fraction further.
x=highlight%283587%2F19980%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What fraction is represented by 0.17952? where the 952 is repeating.


Let fraction be F

             F = 0.17952 ------- eq (i)

          100F = 17.952 -------- Multiplying eq (i) by 100 --------- eq (ii)

      100,000F = 17,952.952 ---- Multiplying eq (i) by 100,000 ----- eq (iii) 

     - 99,900F = - 17,935 ------ Subtracting eq (iii) from eq (ii)

             F = %28-+17935%29%2F-+99900

F, or fraction = highlight_green%283587%2F19980%29

You can do the check!! 



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