new BigDecimal(double) vs new BigDecimal(String)

Question

When BigDecimal is used with an input of double and BigDecimal with an input of String different results seem to appear.

BigDecimal a = new BigDecimal(0.333333333);
BigDecimal b = new BigDecimal(0.666666666);

BigDecimal c = new BigDecimal("0.333333333");
BigDecimal d = new BigDecimal("0.666666666");

BigDecimal x = a.multiply(b);
BigDecimal y = c.multiply(d);

System.out.println(x);
System.out.println(y);

x outputs as

0.222222221777777790569747304508155316795087227497352441864147715340493949298661391367204487323760986328125

while y is

0.222222221777777778

Am I wrong in saying that this is because of double imprecision? But since this is a BigDecimal, shouldn't it be the same?

Answer 1

Am I wrong in saying that this is because of double imprecision?

You are absolutely right, this is exactly because of double's imprecision.

But since this is a BigDecimal, shouldn't it be the same?

No, it shouldn't. The error is introduced the moment you create new BigDecimal(0.333333333), because 0.333333333 constant already has an error embedded in it. At that point there is nothing you can do to fix this representation error: the proverbial horse is out of the barn by then, so it's too late to close the doors.

When you pass a String, on the other hand, the decimal representation matches the string exactly, so you get a different result.