DEADFR  Dead Fraction
Mike is frantically scrambling to finish his thesis at the last minute. He needs to assemble all his research notes into vaguely coherent form in the next 3 days. Unfortunately, he notices that he had been extremely sloppy in his calculations. Whenever he needed to perform arithmetic, he just plugged it into a calculator and scribbled down as much of the answer as he felt was relevant. Whenever a repeating fraction was displayed, Mike simply reccorded the first few digits followed by "...". For instance, instead of "1/3" he might have written down "0.3333...". Unfortunately, his results require exact fractions! He doesn't have time to redo every calculation, so he needs you to write a program (and FAST!) to automatically deduce the original fractions.
To make this tenable, he assumes that the original fraction is always the simplest one that produces the given sequence of digits; by simplest, he means the the one with smallest denominator. Also, he assumes that he did not neglect to write down important digits; no digit from the repeating portion of the decimal expansion was left unrecorded (even if this repeating portion was all zeroes).
Input
There are several test cases. For each test case there is one line of input of the form "0.dddd..." where dddd is a string of 1 to 18 digits, not all zero. A line containing 0 follows the last case.
Output
For each case, output the original fraction.
Example
Input: 0.2... 0.20... 0.474612399... 0 Output: 2/9 1/5 1186531/2500000
hide comments
Amitayush Thakur:
20181201 19:12:02
@lenosey: Mathematically speaking 0.4746124 == 0.4746123999999..... . Infact 1 == 0.9999.... there is a wiki page on that. Read about it here: https://en.wikipedia.org/wiki/0.999... 

lenosey:
20170814 04:31:54
i can't understand the answer of 0.474612399... is 1186531/2500000? 1186531/2500000==0.4746124? Last edit: 20170814 04:32:32 

Shashank Tiwari:
20150829 15:14:03
Let me make problem statement clear ...


kartikay singh:
20141226 09:30:47
need test cases ...


mjh:
20141220 09:54:20
for the ans 1, you should print 1/1.


Hasil Sharma:
20141016 17:49:37
AC :) .. Try not to assume anything from your side .. 

Gannu_raj:
20141007 15:19:58
What should be output for this test case


Bharath Reddy:
20140430 10:40:52
@those getting WA. check whether your code overflows for this case:


nitish rao:
20130630 17:51:31
after a lot of frustration... got an AC...:) try writing the code without using any double type in order to avoid unnecessary rounding offs..(in my algo..).i've done that way.. 

Lalit:
20130523 10:40:50
I think my code is correct and it giving correct output for all the nos that i have checked. still m getting WA..:( my id is 9326947 . plz check it and tell whats wrong with it

Added by:  Camilo Andrés Varela León 
Date:  20061216 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Waterloo Local Contest Sep. 27, 2003 