shunfurh 于 2017.09.05 07:55 提问

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 9 digits, not all zero. A line containing 0 follows the last case.

Output

For each case, output the original fraction.

Note that an exact decimal fraction has two repeating expansions (e.g. 1/5 = 0.2000... = 0.19999...).

Sample Input

0.2...
0.20...
0.474612399...
0

Sample Output

2/9
1/5
1186531/2500000

2个回答

caozhy      2017.09.07 23:47

shen_wei      2017.09.05 15:31

Dead FractionTime Limit: 1000MS Memory Limit: 30000KTotal Submissions: 1198 Accepted: 354DescriptionMike is frantically scrambling to finish his thesis at the la
poj1930 题目意思:给定一个无限循环小数，把它转换成分数。 这个需要一定姿势水平。。。纯循环9做分母，有几个循环数，就有几个9，例如0.3就是9分之3，0.654就是999分之654。。等等混循环把0.228转换成分数(8是循环节) =[（228/1000）+8/9000）] =228/（900+100）+8/9000 =[（228/900）-（228/9000）]+（8/9000）
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 h