Java Double value = 0.01 changes to 0.009999999999

Question

Possible Duplicate:
Why not use Double or Float to represent currency?

I'm writing a basic command-line program in Java for my high school course. We're only working with variables right now. It's used to calculate the amount of bills and coins of whatever type in your change after a purchase. This is my program:

class Assign2c {
    public static void main(String[] args) {
        double cost = 10.990;
        int paid = 20;
        double change = paid - cost;
        int five, toonie, loonies, quarter, dime, nickel, penny;

        five = (int)(change / 5.0);
        change -= five * 5.0;

        toonie = (int)(change / 2.0);
        change -= toonie * 2.0;

        loonies = (int)change;
        change -= loonies;

        quarter = (int)(change / 0.25);
        change -= quarter * 0.25;

        dime = (int)(change / 0.1);
        change -= dime * 0.1;

        nickel = (int)(change / 0.05);
        change -= nickel * 0.05;

        penny = (int)(change * 100);
        change -= penny * 0.01;

        System.out.println("$5   :" + five);
        System.out.println("$2   :" + toonie);
        System.out.println("$1   :" + loonies);
        System.out.println("$0.25:" + quarter);
        System.out.println("$0.10:" + dime);
        System.out.println("$0.05:" + nickel);
        System.out.println("$0.01:" + penny);
    }
}

It should all work but at the last step when there's $0.01 leftover, number of pennies should be 1 but instead, it's 0. After a few minutes of stepping into the code and outputting the change value to the console, I've found out that at the last step when change = 0.01, it changes to 0.009999999999999787. Why is this happening?

Answer 1

its a float(double)

You should not use it to compute money....

I recommend using int values and operate on pennys

Answer 2

I'm sure you know that some fractions' decimal representations terminate (e.g. .01) while some don't (e.g. 2/3=.66666...). The thing is that which fractions terminate changes depending on what base you're in; in particular, .01 doesn't terminate in binary, so even though double provides a lot of precision it can't represent .01 exactly. As others said, using BigDecimal or fixed-point integer computations (converting everything to cents) is probably best for currency; to learn more about floating point, you could start at The Floating-Point Guide- What Every Programmer Should Know About Floating-Point Arithmetic.

Answer 3

As the others already said, do not use doubles for financial calculations.

This paper http://download.oracle.com/docs/cd/E19957-01/806-3568/ncg_goldberg.html (What Every Computer Scientist Should Know About Floating-Point Arithmetic) is a must-read to understand floating point math in computers.

Answer 4

Using double for currency is a bad idea, Why not use Double or Float to represent currency?. I recommend using BigDecimal or doing every calculation in cents.

Answer 5

Floating point numbers are never 100% accurate (not quite true, see comments below). You should never compare them directly. Also integer rounding. The best way to do this would probably be to do it in cents and convert to dollars later (1 dollar == 100 cents). By converting to an integer you are losing precision.

Answer 6

This is a problem that's arisen many times over. The bottom line is that on a computer that uses binary floating point (which Java requires), only fractions in which the denominator is a power of 2 can be represented precisely.

The same problem arises in decimal. 1/3, for example, turns into 0.3333333..., because 3 isn't a factor of 10 (the base we're using in decimal). Likewise 1/17, 1/19, etc.

In binary floating point, the same basic problem arises. The main difference is that in decimal, since 5 is a factor of 10, 1/5 can be represented precisely (and so can multiples of 1/5). Since 5 is not a factor of 2, 1/5 cannot be represented precisely in binary floating point.

Contrary to popular belief, however, some fractions can be represented precisely -- specifically those fractions whose denominators with only 2 as a prime factor (e.g., 1/8 or 1/256 can be represented precisely).