Write a program that converts a decimal to a mixed, simplified fraction.

Sample input:


Sample output:

5 + (1/5)

The code with the shortest length in bytes wins.

  • 5
    \$\begingroup\$ Easy: 1.2345 = 12345/10000. You give me the precision & I'll give you the fraction! \$\endgroup\$ – recursion.ninja Jan 2 '14 at 21:52
  • \$\begingroup\$ Do you mean simplified fractions? \$\endgroup\$ – hkk Jan 2 '14 at 21:53
  • \$\begingroup\$ i meant mixed fractions \$\endgroup\$ – belvi Jan 2 '14 at 21:58
  • \$\begingroup\$ basically: find how many spaces the decimal goes beyond the decimal point (e.g. 2.357 is 3 digits after decimal), then turn it into improper, unsimplified: 2357/1000 and then, have a list of primes, starting at lowest, try to divide both numbers by it without remainder, then try it on that until at least one of the numbers is a prime and the other is not divisible by that number, and you're done \$\endgroup\$ – markasoftware Jan 2 '14 at 22:04
  • 2
    \$\begingroup\$ 5.2 != 5+1/2... \$\endgroup\$ – Kevin Jan 2 '14 at 22:28

11 Answers 11


Ruby, 43

y=gets.to_r;puts"#{y.to_i} + (#{y-y.to_i})"

Pretty straightforward.

  • \$\begingroup\$ Interesting solution. I'm honestly surprised you can make such short program with correct output format. \$\endgroup\$ – Konrad Borowski Jan 3 '14 at 17:47
  • \$\begingroup\$ Ruby has a lot of Lispy features and the Rational class is probably one of the lesser-known ones. However, if the input is a float you're liable to get something like "2 + (1499999999999999/5000000000000000)" \$\endgroup\$ – Ibrahim Tencer Jan 4 '14 at 4:01

GolfScript, 40


Requires no line terminator in the input. Can probably be golfed further.


Golf-Basic 84, 32 characters

Executed from a TI-84 calculator


Mathematica 73

No cigar this time. Numerator, Denominator and Rationalize are big words.






GTB, 28

  • \$\begingroup\$ The source code for your compiler cannot be run since iX2Web is not available. The link in your site is bad as well. \$\endgroup\$ – mbomb007 Apr 13 '15 at 20:58

OK, this isn't the shortest. But the proper way to convert decimals to fractions is to use continued fractions.

#include <stdio.h>
#include <string.h>
#include <math.h>

int main(int argc, char **argv) {
  double f = 152/147.;
  int temp, i, cf[50], n=0, d=1;
  double prec = 1e-6;


  for (i=0;i<50 && prec<1;i++) {
    cf[i] = f;
/* Next line assumes division by zero evaluates to inf */
    f = 1/(f-cf[i]);

  for (;i>=0;i--) {
    temp = n;
    n = n*cf[i] + d;
    d = temp;
  if (cf[0] == 0)
    printf("%d %d/%d\n",cf[0],d,n);


Perl 6 (53 bytes)

Does the output in right, expected format. Would be way shorter if output in invalid format would be allowed. This gets a number, converts it to rational. nude method returns denominator and numerator (there are separate denominator and numerator methods, but they are crazily long.

[] is a reduce operator which takes operator between square brackets, and in this case, I use it to shorten the code (so I wouldn't have to specify both array elements, because they are already in correct order (but if they wouldn't, there are R operators (like R/, R%, Rdiv, and Rmod) that reverse the order of arguments for operator)). {} in double quotes puts the result of code in string (like #{} in Ruby).

my \ is declaration of sigilless variable. In this case it doesn't save characters, but it doesn't waste them either, so why not use it. I could have used my@, and it would use identical number of characters.

my \n=get.Rat.nude;say "{[div] n} + ({[%] n}/{n[1]})"

Sample output (just to show the correct format):

~ $ perl6 -e 'my \n=get.Rat.nude;say "{[div] n} + ({[%] n}/{n[1]})"'
42 + (21/50)

If negative number support is needed, this would work (2 bytes more).

~ $ perl6 -e 'my \n=get.Rat.nude;say "{[div] n} + ({[mod] n}/{n[1]})"'
-42 + (-21/50)

python 3, 84

from fractions import*
print("%s + (%s)"%(a,Fraction("."+b)))
  • \$\begingroup\$ Doesn't return the output in correct format. + should be returned (but otherwise, it's close to expected format). \$\endgroup\$ – Konrad Borowski Jan 3 '14 at 7:03
  • \$\begingroup\$ @GlitchMr Edited the format. \$\endgroup\$ – Wasi Jan 3 '14 at 7:52
  • \$\begingroup\$ Also, there are parens. Dunno why, but the OP put them. \$\endgroup\$ – Konrad Borowski Jan 3 '14 at 12:42
  • \$\begingroup\$ @GlitchMr Added those creepy parens. Now the code size raised to 84 :-( \$\endgroup\$ – Wasi Jan 3 '14 at 12:58

R, several lines

How about the way they tought us at grammar school?

  gcd=function(a,b)if(!b)a else gcd(b,a%%b)
  cat(a[1]," + (",x/d,"/",p/d,")",sep="");

Vaguely: works for positive decimals with finite decimal fraction.

> f("23.872")
23 + (109/125)

Input must be a string matching "[0-9]+\.[0-9]+" regular expression.



Isn't pretty, but whatever

import Data.Ratio
main=let r '%'='/';r c=c in interact$(\(x,y)->show x++" + "++map r(show$approxRational y 1e-9)).properFraction.read

kind of cheating, but pressing these characters in a mathematica notebook looks it up in wolfram alpha, which gives the mixed fraction form among other information


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