Convert a repeated decimal to a fraction This question doesn't need to apply to just terminating decimals - repeating decimals can also be converted to fractions via an algorithm.

Your task is to make a program that takes a repeated decimal as input, and output the corresponding numerator and denominator (in lowest terms) that produces that decimal expansion. Fractions greater than 1 should be represented as improper fractions like 9/5. You can assume that input will be positive.

The repeated decimal will be given in this format:

5.3.87


with everything after the second dot repeated, like this:

5.3878787878787...


Your program will output two integers representing the numerator and denominator, separated by a slash (or the equivalent form in your language if you do not output plain text):

889/165


Note that terminating decimals will have nothing after the second dot, and decimals with no non-repeating decimal portion will have nothing between the two dots.

Test cases

These test cases cover all of the required corner cases:

0..3 = 1/3
0.0.3 = 1/30
0.00.3 = 1/300
0.6875. = 11/16
1.8. = 9/5
2.. = 2/1
5..09 = 56/11
0.1.6 = 1/6
2..142857 = 15/7
0.01041.6 = 1/96
0.2.283950617 = 37/162
0.000000.1 = 1/9000000
0..9 = 1/1
0.0.9 = 1/10
0.24.9 = 1/4


If you wish, you can also assume that fractions without integer parts have nothing to the left of the first dot. You can test that with these optional test cases:

.25. = 1/4
.1.6 = 1/6
..09 = 1/11
.. = 0/1
Perl 6 (93 101 100 80 68 66 bytes)

$/=split ".",get;say ($0+($1+$2/(9 x$2.comb||1))/10**$1.comb).nude


The size was increased to handle nothing, instead of just failing. Mouq proposed to use $/, so it's now being used, and the code is 20 bytes shorter. Ayiko proposed replacing / with , so the code is even shorter (by 12 bytes). Then Mouq proposed replacing chars with comb (in numeric context, they are identical, because list of characters after conversion to number is number of characters).

Sample output:

$ perl6 script.p6
5.3.87
889 165
$ perl6 script.p6
2.0.0
2 1
$ perl6 script.p6
0..3
1 3
$ perl6 script.p6
0.0.3
1 30
$ perl6 script.p6
0.0.0
0 1
$ perl6 script.p6
0.1.6
1 6
$ perl6 script.p6
0.01041.6
1 96
$ perl6 script.p6
0.2.283950617
37 162
$ perl6 script.p6
123.456.789
41111111 333000