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Convert given Decimal number into an irreducible Fraction

  • Difficulty Level : Hard
  • Last Updated : 12 May, 2021

Given a decimal number as N, the task is to convert N into an equivalent irreducible fraction.

An irreducible fraction is a fraction in which numerator and denominator are co-primes i.e., they have no other common divisor other than 1. 

Examples:

Input: N = 4.50
Output: 9/2 
Explanation:
9/2 in decimal is written as 4.5

Input: N = 0.75
Output: 3/4
Explanation:
3/4 in decimal is written as 0.75



Approach: Follow the steps given below to solve the problem.

  • Fetch integral value and fractional part of the decimal number ‘n’.
  • Consider the precision value to be 109 to convert the fractional part of the decimal to an integral equivalent.
  • Calculate GCD of the integral equivalent of fractional part and precision value.
  • Calculate numerator by dividing the integral equivalent of fractional part by GCD value. Calculate the denominator by dividing the precision value by GCD value.
  • From the obtained mixed fraction, convert it into an improper fraction.

For example N = 4.50, integral value = 4  and  fractional part = 0.50 
           
Consider precision value to be (109) that is precision value = 1000000000 
           
Calculate GCD(0.50 *  109, 109) = 500000000 
           
Calculate numerator = (0.50 * 10^9) / 500000000 = 1 and denominator = 10^9/ 500000000 = 2 
           
Convert mixed fraction into improper fraction that is fraction = ((4 * 2) + 1) / 2 = 9/2 
 

Below is the implementation of the above approach:

C++




// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;
 
// Recursive function to
// return GCD of a and b
long long gcd(long long a, long long b)
{
    if (a == 0)
        return b;
    else if (b == 0)
        return a;
    if (a < b)
        return gcd(a, b % a);
    else
        return gcd(b, a % b);
}
 
// Function to convert decimal to fraction
void decimalToFraction(double number)
{
    // Fetch integral value of the decimal
    double intVal = floor(number);
 
    // Fetch fractional part of the decimal
    double fVal = number - intVal;
 
    // Consider precision value to
    // convert fractional part to
    // integral equivalent
    const long pVal = 1000000000;
 
    // Calculate GCD of integral
    // equivalent of fractional
    // part and precision value
    long long gcdVal
        = gcd(round(fVal * pVal), pVal);
 
    // Calculate num and deno
    long long num
        = round(fVal * pVal) / gcdVal;
    long long deno = pVal / gcdVal;
 
    // Print the fraction
    cout << (intVal * deno) + num
         << "/" << deno << endl;
}
 
// Driver Code
int main()
{
    double N = 4.5;
 
    decimalToFraction(N);
 
    return 0;
}

C




// C implementation of the above approach
#include <math.h>
#include <stdio.h>
 
int gcfFinder(int a, int b)
{ // gcf finder
    int gcf = 1;
    for (int i = 1; i <= a && i <= b; i++)
    {
        if (a % i == 0 && b % i == 0)
        {
            gcf = i;
        }
    }
    return gcf;
}
 
int shortform(int* a, int* b)
{
    for (int i = 2; i <= *a && i <= *b; i++)
    {
        if (*a % i == 0 && *b % i == 0)
        {
            *a = *a / i;
            *b = *b / i;
        }
    }
    return 0;
}
 
// Driver Code
int main(void)
{
    // converting decimal into fraction.
    double a = 4.50;
 
    int c = 10000;
    double b = (a - floor(a)) * c;
    int d = (int)floor(a) * c + (int)(b + .5f);
 
    while (1)
    {
        if (d % 10 == 0)
        {
            d = d / 10;
            c = c / 10;
        }
        else
            break;
    }
    int* i = &d;
    int* j = &c;
    int t = 0;
    while (t != 1)
    {
        int gcf = gcfFinder(d, c);
        if (gcf == 1)
        {
            printf("%d/%d\n", d, c);
            t = 1;
        }
        else
        {
            shortform(i, j);
        }
    }
    return 0;
}
// this code is contributed by harsh sinha username-
// harshsinha03

Java




// Java program for the above approach
import java.util.*;
 
class GFG{
     
// Recursive function to
// return GCD of a and b
static long gcd(long a, long b)
{
    if (a == 0)
        return b;
    else if (b == 0)
        return a;
    if (a < b)
        return gcd(a, b % a);
    else
        return gcd(b, a % b);
}
     
// Function to convert decimal to fraction
static void decimalToFraction(double number)
{
   
    // Fetch integral value of the decimal
    double intVal = Math.floor(number);
  
    // Fetch fractional part of the decimal
    double fVal = number - intVal;
  
    // Consider precision value to
    // convert fractional part to
    // integral equivalent
    final long pVal = 1000000000;
  
    // Calculate GCD of integral
    // equivalent of fractional
    // part and precision value
    long gcdVal = gcd(Math.round(
                      fVal * pVal), pVal);
   
    // Calculate num and deno
    long num = Math.round(fVal * pVal) / gcdVal;
    long deno = pVal / gcdVal;
  
    // Print the fraction
    System.out.println((long)(intVal * deno) +
                           num + "/" + deno);
}
   
// Driver Code
public static void main(String s[])
{
    double N = 4.5;
    decimalToFraction(N);
}   
}
 
// This code is contributed by rutvik_56

Python3




# Python3 program for the above approach
from math import floor
 
# Recursive function to
# return GCD of a and b
def gcd(a, b):
     
    if (a == 0):
        return b
    elif (b == 0):
        return a
    if (a < b):
        return gcd(a, b % a)
    else:
        return gcd(b, a % b)
 
# Function to convert decimal to fraction
def decimalToFraction(number):
     
    # Fetch integral value of the decimal
    intVal = floor(number)
 
    # Fetch fractional part of the decimal
    fVal = number - intVal
 
    # Consider precision value to
    # convert fractional part to
    # integral equivalent
    pVal = 1000000000
 
    # Calculate GCD of integral
    # equivalent of fractional
    # part and precision value
    gcdVal = gcd(round(fVal * pVal), pVal)
 
    # Calculate num and deno
    num= round(fVal * pVal) // gcdVal
    deno = pVal // gcdVal
 
    # Print the fraction
    print((intVal * deno) + num, "/", deno)
 
# Driver Code
if __name__ == '__main__':
     
    N = 4.5
 
    decimalToFraction(N)
 
# This code is contributed by mohit kumar 29

C#




// C# program for the above approach
using System;
 
class GFG{
     
// Recursive function to
// return GCD of a and b
static long gcd(long a, long b)
{
    if (a == 0)
        return b;
    else if (b == 0)
        return a;
    if (a < b)
        return gcd(a, b % a);
    else
        return gcd(b, a % b);
}
     
// Function to convert decimal to fraction
static void decimalToFraction(double number)
{
 
    // Fetch integral value of the decimal
    double intVal = Math.Floor(number);
 
    // Fetch fractional part of the decimal
    double fVal = number - intVal;
 
    // Consider precision value to
    // convert fractional part to
    // integral equivalent
    long pVal = 1000000000;
 
    // Calculate GCD of integral
    // equivalent of fractional
    // part and precision value
    long gcdVal = gcd((long)Math.Round(
                    fVal * pVal), pVal);
 
    // Calculate num and deno
    long num = (long)Math.Round(fVal * pVal) / gcdVal;
    long deno = pVal / gcdVal;
 
    // Print the fraction
    Console.WriteLine((long)(intVal * deno) +
                          num + "/" + deno);
}
 
// Driver Code
public static void Main(String []s)
{
    double N = 4.5;
     
    decimalToFraction(N);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
 
// Javascript program to implement
// the above approach
 
// Recursive function to
// return GCD of a and b
function gcd(a, b)
{
    if (a == 0)
        return b;
    else if (b == 0)
        return a;
    if (a < b)
        return gcd(a, b % a);
    else
        return gcd(b, a % b);
}
      
// Function to convert decimal to fraction
function decimalToFraction(number)
{
    
    // Fetch letegral value of the decimal
    let letVal = Math.floor(number);
   
    // Fetch fractional part of the decimal
    let fVal = number - letVal;
   
    // Consider precision value to
    // convert fractional part to
    // letegral equivalent
    let pVal = 1000000000;
   
    // Calculate GCD of letegral
    // equivalent of fractional
    // part and precision value
    let gcdVal = gcd(Math.round(
                      fVal * pVal), pVal);
    
    // Calculate num and deno
    let num = Math.round(fVal * pVal) / gcdVal;
    let deno = pVal / gcdVal;
   
    // Print the fraction
    document.write((letVal * deno) +
                           num + "/" + deno);
}
    
    
    // Driver Code
           
    let N = 4.5;
    decimalToFraction(N);
 
</script>
Output: 
9/2

Time complexity: O(log min(a, b)) 
Auxiliary space: O(1)

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