What's with this output from a double?

Question

I am getting strange output when I add doubles together. Can someone tell me why I'm getting repeating decimals when I am adding 0.1 every time?

I have worked out the formula for adding these numbers together and I have done this myself on paper up to 3.3...

The sum of all numbers (decreasing by 1 tenth) from 3.3 to 1 equals 51.6

3.3
3.2
3.1 +
3.0
...
1.0
_
51.6

There is an easier way to calculate this using two formulas:

The linear formula for the increasing number: Y = 0.1X + 1
And the sum of increasing numbers formula: [X * (Y + 1)]/2 = total

first solve for Y using any number (in this case 100)

11 = 0.1(100) + 1

Then solve for the total using X and Y

[100 * (11+1)]/2 = 600

The output of the following code should be 600 I believe. There is no question that it should not have a repeating decimal. What am I doing wrong here? There must be something I missed.

public static void main(String[] args) {

      int days = 100;
      double inc = 0.1;
      double init = 1;
      double total = 0;

      for (int i = 1; i <= days; i++) {
          if (i == 1) {
            total = total + init;
          } else {
            init = init + inc;
            total = total + init;
          }
      }
      System.out.println("Total: " + total);
      System.out.println("Daily: " + init);
  }

Answer 1

Please read the link that Don Roby posted. In essence, double precision is not a good way to represent fractions. A number like 0.1 does not have an exact representation in binary float notation - because floating point numbers are written as "something times two to the power something else". And you cannot solve that exactly for 0.1. Thus, you are really getting a slightly smaller number - actually

0.0999999999999998

And that missing amount is enough to mess up the math…

See Jon Skeet's very excellent answer on this topic: https://stackoverflow.com/a/1089026/1967396