Why does casting to float produce correct result in java?

Question

System.out.println(2.00-1.10)

and

System.out.println((double)(2.00-1.10)) 

both output same result 0.8999999999999999, but

System.out.println((float)(2.00-1.10)) 

outputs 0.9.

Perhaps by default Java performs calculations in double, then why does downcasting corrects result?

And if 1.1 is converted to 1.100000000000001 in double then why does

System.out.println((double)(1.10)) outputs 1.1 only.

EDIT: To get why this happens we need to understand both answers. First the canonical representation is actually different at lower level. Next how the return value of toString is changed/rounded off/matched with the nearest double of argument.

Answer 1

0.9 is not representable as a double or a float. The internal details of floating point calculation has been answered in various posts on SO, such as: Is floating point math broken?.

In your specific example, you can see the double and float that are closest to 0.9 with this code:

System.out.println(new BigDecimal(0.9d));
System.out.println(new BigDecimal(0.9f));

which outputs the canonical double and float representations of 0.9:

0.90000000000000002220446049250313080847263336181640625
0.89999997615814208984375

Now when you calculate 2.0 - 1.1, the result is:

System.out.println(new BigDecimal(2.0-1.1));

0.899999999999999911182158029987476766109466552734375

You can see that it is not the canonical representation of 0.9 hence you get a different result.

However float precision is not as good and:

System.out.println(new BigDecimal((float) (2.0-1.1)));

0.89999997615814208984375

returns the same number as the canonical representation of 0.9f.