# Find the Nth digit in the proper fraction of two numbers

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…

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Initialize an integer variable res that stores the resultant Nth digit. Now, while N > 0 do the following:

1. Decrement N by 1.
2. To compute the digit, update the value P = P * 10.
3. Compute res = P / Q and update P = P % Q.

Finally, print the res.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `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 code ` `int` `main() ` `{ ` `    ``int` `p = 1, q = 2, N = 1; ` ` `  `    ``cout << findNthDigit(p, q, N); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `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(String args[])  ` `    ``{  ` `        ``int` `p = ``1``, q = ``2``, N = ``1``;  ` `     `  `        ``System.out.println(findNthDigit(p, q, N));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# 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 code  ` `if` `__name__ ``=``=` `"__main__"` `: ` `     `  `    ``p ``=` `1``; q ``=` `2``; N ``=` `1``; ` `    ``print``(findNthDigit(p, q, N));  ` ` `  `# This code is contributed by kanugargng `

## C#

 `// C# implementation of the approach ` `using` `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 `

Output:

```5
```

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