Count number of digits after decimal on dividing a number

We are given two numbers A and B. We need to calculate the number of digits after decimal. If in case the numbers are irrational then print “INF”.

Examples:

```Input  : x = 5, y = 3
Output : INF
5/3 = 1.666....

Input :  x = 3, y = 6
Output : 1
3/6 = 0.5
```

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

The idea is simple we follow school division and keep track of remainders while dividing one by one. If remainder becomes 0, we return count of digits seen after decimal. If remainder repeats, we return INF.

C++

 `// CPP program to count digits after dot when a ` `// number is divided by another. ` `#include ` `using` `namespace` `std; ` ` `  `int` `count(``int` `x, ``int` `y) ` `{ ` `    ``int` `ans = 0;  ``// Initialize result ` `     `  `    ``unordered_map<``int``, ``int``> m; ` `     `  `    ``// calculating remainder ` `    ``while` `(x % y != 0) { ` ` `  `        ``x = x % y; ` ` `  `        ``ans++; ` ` `  `        ``// if this remainder appeared before then  ` `        ``// the numbers are irrational and would not ` `        ``// converge to a solution the digits after ` `        ``// decimal will be infinite ` `        ``if` `(m.find(x) != m.end())  ` `            ``return` `-1; ` ` `  `        ``m[x] = 1; ` `        ``x = x * 10; ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `res = count(1, 2); ` `    ``(res == -1)? cout << ``"INF"` `: cout << res; ` ` `  `    ``cout << endl; ` `    ``res = count(5, 3); ` `    ``(res == -1)? cout << ``"INF"` `: cout << res; ` ` `  `    ``cout << endl; ` `    ``res = count(3, 5); ` `    ``(res == -1)? cout << ``"INF"` `: cout << res; ` `    ``return` `0; ` `} `

Java

 `// Java program to count digits after dot when a ` `// number is divided by another. ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `static` `int` `count(``int` `x, ``int` `y) ` `{ ` `    ``int` `ans = ``0``; ``// Initialize result ` `     `  `    ``Map m = ``new` `HashMap<>(); ` `     `  `    ``// calculating remainder ` `    ``while` `(x % y != ``0``)  ` `    ``{ ` ` `  `        ``x = x % y; ` ` `  `        ``ans++; ` ` `  `        ``// if this remainder appeared before then  ` `        ``// the numbers are irrational and would not ` `        ``// converge to a solution the digits after ` `        ``// decimal will be infinite ` `        ``if` `(m.containsKey(x))  ` `            ``return` `-``1``; ` ` `  `        ``m.put(x, ``1``); ` `        ``x = x * ``10``; ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``int` `res = count(``1``, ``2``); ` `    ``if``((res == -``1``)) ` `        ``System.out.println(``"INF"``); ` `    ``else` `        ``System.out.println(res);  ` ` `  `    ``res = count(``5``, ``3``); ` `    ``if``((res == -``1``)) ` `        ``System.out.println(``"INF"``); ` `    ``else` `        ``System.out.println(res);  ` `     `  `    ``res = count(``3``, ``5``); ` `    ``if``((res == -``1``)) ` `        ``System.out.println(``"INF"``); ` `    ``else` `        ``System.out.println(res); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Python3

 `# Python3 program to count digits after dot  ` `# when a number is divided by another. ` `def` `count(x, y): ` `    ``ans ``=` `0` `# Initialize result ` ` `  `    ``m ``=` `dict``() ` ` `  `    ``# calculating remainder ` `    ``while` `x ``%` `y !``=` `0``: ` `        ``x ``%``=` `y ` ` `  `        ``ans ``+``=` `1` ` `  `        ``# if this remainder appeared before then ` `        ``# the numbers are irrational and would not ` `        ``# converge to a solution the digits after ` `        ``# decimal will be infinite ` `        ``if` `x ``in` `m: ` `            ``return` `-``1` ` `  `        ``m[x] ``=` `1` `        ``x ``*``=` `10` ` `  `    ``return` `ans ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``res ``=` `count(``1``, ``2``) ` ` `  `    ``print``(``"INF"``) ``if` `res ``=``=` `-``1` `else` `print``(res) ` ` `  `    ``res ``=` `count(``5``, ``3``) ` `    ``print``(``"INF"``) ``if` `res ``=``=` `-``1` `else` `print``(res) ` ` `  `    ``res ``=` `count(``3``, ``5``) ` `    ``print``(``"INF"``) ``if` `res ``=``=` `-``1` `else` `print``(res) ` ` `  `# This code is contributed by ` `# sanjeev2552 `

C#

 `// C# program to count digits after dot when a ` `// number is divided by another.  ` `using` `System; ` `using` `System.Collections.Generic; ` `     `  `class` `GFG  ` `{ ` ` `  `static` `int` `count(``int` `x, ``int` `y) ` `{ ` `    ``int` `ans = 0; ``// Initialize result ` `     `  `    ``Dictionary<``int``,``int``> m = ``new` `Dictionary<``int``,``int``>(); ` `     `  `    ``// calculating remainder ` `    ``while` `(x % y != 0)  ` `    ``{ ` ` `  `        ``x = x % y; ` ` `  `        ``ans++; ` ` `  `        ``// if this remainder appeared before then  ` `        ``// the numbers are irrational and would not ` `        ``// converge to a solution the digits after ` `        ``// decimal will be infinite ` `        ``if` `(m.ContainsKey(x))  ` `            ``return` `-1; ` ` `  `        ``m.Add(x, 1); ` `        ``x = x * 10; ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args)  ` `{ ` `    ``int` `res = count(1, 2); ` `    ``if``((res == -1)) ` `        ``Console.WriteLine(``"INF"``); ` `    ``else` `        ``Console.WriteLine(res);  ` ` `  `    ``res = count(5, 3); ` `    ``if``((res == -1)) ` `        ``Console.WriteLine(``"INF"``); ` `    ``else` `        ``Console.WriteLine(res);  ` `     `  `    ``res = count(3, 5); ` `    ``if``((res == -1)) ` `        ``Console.WriteLine(``"INF"``); ` `    ``else` `        ``Console.WriteLine(res); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```1
INF
1
```

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