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I don't understand why the output of 100 will the the value you give, I thought it should be 1 / (2 * 100) = 0.005.
Here is my code

import java.util.Scanner;

public class Solution{
	public String getAnswer(int input){
		input *= 2;
		int numerator = 1;
		StringBuilder sb = new StringBuilder();
		sb.append("0.");
		while(numerator != 0){
			//times 10 first
			numerator *= 10;
			//if numerator is less than denomerator
			//we have to times 10 again and again
			//and each time, we have to append a 0 
			//to the answer
			while(numerator < input){
				numerator *= 10;
				sb.append("0");
			}
			sb.append(numerator / input);
			numerator = numerator % input;
		}
		return sb.toString();
}

	public static void main(String[] args){
		int T;
		Scanner scanner = new Scanner(System.in);
		Solution s = new Solution();
		T = scanner.nextInt();
		for(int i  = 0; i < T; ++i){
			int input = scanner.nextInt();
			System.out.println(s.getAnswer(input));
		}
	}
}

import sys

file = open('input')
for line in file:
    denominator = 2*int(line)
    numerator = 1 
    print('0.', end='')
    rem = -1
    while(rem != 0):
        numerator = numerator*10
        while numerator < denominator:
            numerator = numerator*10
            print('0', end='')
        else: 
            div = numerator / denominator
            rem = numerator % denominator
            print(int(div), end='')
            numerator=rem
    print()

I don't really understand why this is such a hard task, this is grade 2 math.
C#

static string recurs(int currnum, int divider, string curr)
        {
            currnum *= 10;
            int remain = currnum % divider;
            currnum /= divider;
            curr += currnum.ToString();
            Console.Write(currnum.ToString());
            if (remain == 0)
                return curr;
            else
                recurs(remain, divider, curr);
            return curr;
        }
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int number = n * 2;
            Console.Write("0.");
            recurs(1, number, "0.");
            Console.WriteLine();
            Console.ReadLine();
        }

Guys, you have not understood the problem, its not 1/(2 x n) , its 1/(2 to the power n), its complicated calculation

1/2^n can be written as (5/10)^n. now calculating 5^n
double d=Math.pow(5,n);(or can be done in logn time)(power of 5 will never end in 0)
int length=String.valueOf(d).length()
numberOfZeroseBefore=n-length

System.out.println(new BigDecimal(1 / Math.pow(2, n)).toPlainString());

System.out.println(new BigDecimal(1 / Math.pow(2, 100)).toPlainString());

System.out.println(new BigDecimal(1 / Math.pow(2, 100)).toPlainString());