Simple arithmatic error??? what am i doing wrong?

Question

java is not multiplying large numbers correctly??
run the following program:
public class Test {
  public static void main(String[] args) {
    System.out.println("testing arithmatic.....");
    double a = (double) 27051900;
    float  b = (float) 56.26;
    int    c = (int) (((double) a) * ((float) b));
    System.out.println(a + " * " + b + " = " + c);
    System.out.println("trusty calculator says correct answer: _1,521,939,894_");
    System.our.println("java is off by: " + (1521939894 - c));
    double x = (double) 12;
    float  y = (float) 6;
    int z = (int) (((double) x) * ((float) y));
    System.out.println(x + "*" y + " = " + z);
    System.out.println("correct answer: _72_ [correct]");
    System.out.println("___end test___");
}i am mostly new to java.
what could be causing this strange behaviour?

Answer 1

The Java primitive data type float is 4 bytes, or 32 bits:
1 bit Sign 8 bit exponent 23 bit mantissa
So you result have not be more than 8 388 608 when you operate with float.
Result can be more, but in this case you will lost first digits.
So to receive correct result in this case you have use double.
If you change float to double result will be correct.
you can see :
public class test {
public static void main(String[] args) {
System.out.println("testing arithmatic.....");
double a = (double)27051900;
double b = (double)56.26;
double c = (int)(((double) a) * ((double) b));
//(int) (((double) a) * ((float) b));
System.out.println(a);
System.out.println(b);
System.out.println(a*b);
System.out.println(c);
System.out.println(a + " * " + b + " = " + c);
System.out.println("trusty calculator says correct answer: _1,521,939,894_");
System.out.println("java is off by: " + (1521939894 - c));
double x = (double) 12;
float y = (float) 6;
int z = (int) (((double) x) * ((float) y));
System.out.println(x + "*" y " = " + z);
System.out.println("correct answer: _72_ [correct]");
System.out.println("___end test___");
Result:
init:
deps-jar:
Compiling 1 source file to C:\Apache\htdocs\petals\Java\JavaApplication1\build\classes
compile:
run:
testing arithmatic.....
2.70519E7
56.26
1.521939894E9
1.521939894E9
2.70519E7 * 56.26 = 1.521939894E9
trusty calculator says correct answer: _1,521,939,894_
java is off by: 0.0
12.0*6.0 = 72
correct answer: _72_ [correct]
___end test___
BUILD SUCCESSFUL (total time: 0 seconds)