Is there any primitive type that can contain more than one digit after decimal point?

Question

In a program, I need to display the approximate PI value, which is close to 3.141592653. The program is from The Art and Science of Java Chapter 6 Exercise 3.

Let me outline the exercise. Imagine there is a circle with radius r inscribed inside a square with length of 2r. If a dart is threw in a random fashion, the probability that the dart will fall in the circle is the ratio between the area of the circle and the square, which is PI*r^2/4*r^2, which is the same as PI/4. As a result, the more experiments, the more precise the the value of PI is. Now imagine we are doing it in a coordinates. Randomly choose 2 number, x and y each between -1 and 1. If x^2 + y^2 < 1, the coordinate point will fall into the circle with 1 radius centered in the middle of the coordinates.

Here is the program:

import acm.program.*;

import acm.util.*;

public class ApproxPIValue extends ConsoleProgram{

public void run() {
    int total = 0; //calculating the time the dart falls into the circle.
    for (int a = 0; a < 10000; a++) {
        double x = rgen.nextDouble(-1.0, 1.0);
        double y = rgen.nextDouble(-1.0, 1.0);
        if ((Math.pow(x, 2) + Math.pow(y, 2)) < 1) {
            total++;
        }
    }
    println((double) (total / 10000)*4); // as I mentioned above, the result would be the approximate value of PI/4. By multiplying the result with 4, get the approximate PI value.//
}


/* set RandomGenerator as an instance variable. */
private RandomGenerator rgen = new RandomGenerator();
}

Another question is, is there anyway to print a String without extending any class. As you may notice in the code, I extends ConsoleProgram, which contains the println method. I know there is another method called System.out.print, but when I use it, it doesn't work, even Eclipse doesn't give any warning.

Answer 1

1. To the question in the title: a double has precision to 15 significant digits, irrespective of where the decimal point is.

2. In this code

   (double) (total / 10000)*4)
   

   you cast the resut of integer operations to a double. The result has 15 significant digits, but the number it represents is an integer. One way to correct is

   (total / 10_000.0) * 4
   

   (no need to convert to double explicitly).

3. Use System.out.println() to immediately see the result on-screen. The PrintStream referred to by System.out is a buffered stream which means it doesn't propagate each character to the screen as it is written. It will flush either when the buffer is full or at the sight of a newline character. This is why System.out.print() does not auto-flush.

Answer 2

Since total is an int, total/10000 uses integer division, i.e. it rounds to zero. You seem to try to use floating point division by casting to double, but the actual division happens before the cast is done. Change that line to

println(((double) total / 10000) *4); 

to fix this.

BTW: Java's double has about 16 significant digits.

Answer 3

Re-reading your question, I suspect the problem is this line:

println((double) (total / 10000)*4);

You are dividing one integer with another, which will result in an integer. You then cast that to a double, but by then the damage is done.

To solve this, force the compiler to treat the 10000 value as a double. This will ensure the result is a double.

println((total / 10000d)*4);