Find the Nth digit in the proper fraction of two numbers - GeeksforGeeks

18 Nov, 2021
Given three integers P, Q and N where P < Q, the task is to compute the fraction value of P / Q and find the Nth digit after the decimal.Example  
Input: P = 1, Q = 2, N = 1 Output: 5 (1 / 2) = 0.5 and 5 is the first digit after the decimal.Input: P = 5, Q = 6, N = 5 Output: 3 (5 / 6) = 0.833333333...  
 
Approach: Initialize an integer variable res that stores the resultant Nth digit. Now, while N > 0 do the following:  
Decrement N by 1.To compute the digit, update the value P = P * 10.Compute res = P / Q and update P = P % Q.
Decrement N by 1.
To compute the digit, update the value P = P * 10.
Compute res = P / Q and update P = P % Q.
Finally, print the res.Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std; // Function to print the Nth digit// in the fraction (p / q)int findNthDigit(int p, int q, int N){    // To store the resultant digit    int res;     // While N > 0 compute the Nth digit    // by dividing p and q and store the    // result into variable res    // and go to next digit    while (N > 0) {        N--;        p *= 10;        res = p / q;        p %= q;    }    return res;} // Driver codeint main(){    int p = 1, q = 2, N = 1;     cout << findNthDigit(p, q, N);     return 0;}
// Java implementation of the approachclass GFG{     // Function to print the Nth digit    // in the fraction (p / q)    static int findNthDigit(int p,                            int q, int N)    {        // To store the resultant digit        int res = 0;             // While N > 0 compute the Nth digit        // by dividing p and q and store the        // result into variable res        // and go to next digit        while (N > 0)        {            N--;            p *= 10;            res = p / q;            p %= q;        }        return res;    }         // Driver code    public static void main(String args[])    {        int p = 1, q = 2, N = 1;             System.out.println(findNthDigit(p, q, N));    }} // This code is contributed by AnkitRai01
# Python3 implementation of the approach # Function to print the Nth digit# in the fraction (p / q)def findNthDigit(p, q, N) :     # While N > 0 compute the Nth digit    # by dividing p and q and store the    # result into variable res    # and go to next digit    while (N > 0) :        N -= 1;        p *= 10;        res = p // q;        p %= q;     return res; # Driver codeif __name__ == "__main__" :         p = 1; q = 2; N = 1;    print(findNthDigit(p, q, N)); # This code is contributed by kanugargng
// C# implementation of the approachusing System; class GFG{     // Function to print the Nth digit    // in the fraction (p / q)    static int findNthDigit(int p, int q, int N)    {        // To store the resultant digit        int res = 0;             // While N > 0 compute the Nth digit        // by dividing p and q and store the        // result into variable res        // and go to next digit        while (N > 0)        {            N--;            p *= 10;            res = p / q;            p %= q;        }        return res;    }         // Driver code    public static void Main()    {        int p = 1, q = 2, N = 1;             Console.WriteLine(findNthDigit(p, q, N));    }} // This code is contributed by AnkitRai01
<script>      // JavaScript implementation of the approach       // Function to print the Nth digit      // in the fraction (p / q)      function findNthDigit(p, q, N)      {               // To store the resultant digit        var res;         // While N > 0 compute the Nth digit        // by dividing p and q and store the        // result into variable res        // and go to next digit        while (N > 0)        {          N--;          p *= 10;          res = parseInt(p / q);          p %= q;        }        return res;      }       // Driver code      var p = 1,        q = 2,        N = 1;      document.write(findNthDigit(p, q, N));             // This code is contributed by rdtank.    </script>
5
Time Complexity: O(N)
Auxiliary Space: O(1)
kanugargng
ankthon
rdtank
rohitkumarsinghcna
Fraction
number-digits
Mathematical
Mathematical
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