Multiplying two numbers using BigDecimal returns a wrong value

Question

Executing the following code:

new BigDecimal(0.06 * 3).toString() 

returns 0.179999999999999993338661852249060757458209991455078125 instead of 0.18.

Executing

new BigDecimal(0.06).multiply(new BigDecimal(3)).toString()  

returns the same result.

How is this possible?

Answer 1

You're not multiplying two numbers using BigDecimal. You're multiplying them using double arithmetic, and passing the result to the BigDecimal constructor.

You want:

new BigDecimal("0.06").multiply(new BigDecimal("3")).toString() 

Note that you do want the values in strings - otherwise you're using the double value for 0.06, which isn't exactly 0.06... you've lost information before you start. (You don't really need the string form of 3, but I've done so for consistency.)

For example:

System.out.println(new BigDecimal(0.06)); 

prints

0.059999999999999997779553950749686919152736663818359375 

Answer 2

As Jon Skeet writes above, the reason why you are getting 0.179999999999999993338661852249060757458209991455078125 instead of 0.18 is because 0.06 * 3 is computed as an IEEE 754 double and then this double value is converted to a BigDecimal.

Even though 0.06 looks simple enough in source code, the number 0.06 is not exactly representable as an IEEE 754 double, so what 0.06 actually represents is an approximation of 0.06 equal to 0.059999999999999997779553950749686919152736663818359375. The number 0.06 in decimal notation is not exactly representable because the number equals 0b0.000011110101110000101 in binary notation (where bold represents a repeating digit sequence). The computer must truncate this infinite sequence of binary digits, leading to the 0.0599999... approximation.

As I detailed in my answer to Question regarding IEEE 754, 64 bits double?, you can use ARIBAS' decode_float() function to determine the mantissa and exponent of a floating-point number:

 ==> set_floatprec(double_float). -: 64  ==> set_printbase(2). -: 0y10  ==> decode_float(0.06). -: (0y11110101_11000010_10001111_01011100_00101000_11110101_11000010_10001111,  -0y1000100)  ==> set_printbase(10). -: 10  ==> -0y1000100. -: -68  ==> set_floatprec(128). -: 128  ==> 1/2**4 + 1/2**5 + 1/2**6 + 1/2**7 + 1/2**9 + 1/2**11 + 1/2**12 + 1/2**13 + 1/2**18 + 1/2**20. -: 0.11999_98855_59082_03125_00000_00000_00000_00 

(** is exponentiation in ARIBAS).

And we have 0.06 = Σ _{i = 0..∞}^{0.11999988555908203125} / _{2^{1 + 20 × i}}

You can evaluate this series in a computer algebra system such as Maxima:

 (%i1) sum ( 0.11999988555908203125 / 2 ^ (1 + 20 * i), i, 0, inf ), simpsum; (%o1)                                0.06 

http://maxima-online.org/?inc=r760264757