Math.random and decimals

I really want to understand, thx for help. I've been watching Derek Banas Java Programming video and I got stuck to this:

int randomNumber = (int) (Math.random() * 126) + 1;

The goal is to get a random number from 1 to 126 included. It works but why? How can it output 126?

• If casting int drop decimals.

  126included125(See testing)

• If Math.random() returns 0 - 0.9 inclusive.

The nearest would be like:

1. int randomNumber = (int) (Math.random() * 126) + 1;
2. int randomNumber = (int) (0.99 * 126) + 1;
3. int randomNumber = (int) (124.74) + 1;
4. int randomNumber = (int) 125.74;
5. int randomNumber = 125;

Can someone explain to me why Im wrong.

Testing:

import java.util.*;

public class Random_Number_Test 
{
    public static void main(String[] args) 
    {
        boolean Program_On_Going = true;
        double RoundTest = 125.74;

        while(Program_On_Going)
        {
            int randomNumber = (int) (Math.random() * 126) + 1;

            if(randomNumber == 126)
            {
                System.out.print(randomNumber);
                System.out.print("included");
                Program_On_Going = false;

                System.out.print((int) RoundTest);
            }
            else
            {
                System.out.println(randomNumber);
            }
        }
    }
}

Results

18 30 101 77 101 85 87 6 89 26 20 115 108 13 53 30 85 108 41 110 22 3 38 106 46 102 117 95 36 44 65 87 87 4 114 70 8 120 50 28 60 97 101 25 30 96 4 105 55 29 20 77 105 91 19 81 105 66 1 78 81 48 77 82 11 68 113 1 7 90 104 96 100 70 114 14 125 42 108 16 119 103 70 84 83 42 15 102 45 69 80 123 56 39 115 88 70 111 30 68 19 34 17 24 71 107 81 76 42 80 123 19 54 47 96 58 64 52 61 117 64 103 47 40 60 35 23 90 75 91 29 16 7 15 20 50 85 72 109 85 108 47 54 79 91 102 84 101 5 17 50 115 115 71 67 83 15 99 77 101 20 79 22 25 30 108 46 75 89 80 103 51 61 15 91 9 61 90 11 5 27 36 116 15 14 105 5 95 53 97 55 59 1 81 97 109 77 37 3 84 115 87 15 40 93 61 68 14 93 15 38 55 15 72 48 103 75 42 63 64 61 114 103 17 47 31 102 56 57 113 82 85 48 1 120 117 25 77 101 19 84 54 101 102 2 14 114 105 20 57 70 94 7 27 123 108 109 47 4 28 72 49 86 84 64 86 71 69 33 110 109 19 71 92 49 50 77 29 31 55 62 75 61 8 52 115 69 39 71 107 42 57 92 88 56 88 89 7 123 49 13 107 6 99 21 29 49 3 82 60 104 70 123 91 4 14 57 63 27 126included125