# Unexpected BigDecimal rounding issue

Hi,

Some more not so fun rounding issues.

Using Floats:

((30 / 1.16) * 1.16) == 30
=> true

Cool, so you’d think it would work with BigDecimal:

((30 / BigDecimal(“1.16”)) * BigDecimal(“1.16”)) == 30
=> false

((30 / BigDecimal(“1.16”)) * BigDecimal(“1.16”)).to_s
=> “30.0000000000000000000000002”

I’m clearly missing something here as I thought BigDecimal was supposed
to fix this type of thing.

Tested in:
ruby 1.8.6 (2008-03-03 patchlevel 114) [universal-darwin9.0]
ruby 1.9.1p0 (2009-01-30 revision 21907) [i386-darwin9.6.0]

Can anyone offer an explanation?

Cheers, sam

Hi,

At Wed, 6 May 2009 10:01:54 +0900,
Samuel L. wrote in [ruby-talk:335867]:

((30 / BigDecimal(“1.16”)) * BigDecimal(“1.16”)) == 30
=> false

((30 / BigDecimal(“1.16”)) * BigDecimal(“1.16”)).to_s
=> “30.0000000000000000000000002”

I’m clearly missing something here as I thought BigDecimal was supposed
to fix this type of thing.

BigDecimal is another kind of floating point number, which uses
decimal base instead of binary, but has finite digits.
Therefore, it is impossible to represent exactly a recurring
decimal theoretically.

On Tue, May 5, 2009 at 9:01 PM, Samuel L. [email protected] wrote:

ruby 1.9.1p0 (2009-01-30 revision 21907) [i386-darwin9.6.0]

Can anyone offer an explanation?

BigDecimal is still a kind of float, albeit a decimal float rather
than a binary float.

So it helps with problems when the fractional part of a number can be
expressed exactly as a finite string of decimal digits, but just as
certain fractional parts can’t be expressed exactly as a finite string
of binary digits, there are some which have the same problem when the
base is 10.

For example 1/3 cannot be expressed as a decimal float, no matter how
many digits 0.33333…

Similarly 3000/116 (which is the same as 30/1.16) can’t be expressed
by a finite sequence of decimal digits.

It comes out as

25.862068965517241379310344827[5862068965517241379310344827]…

where the digits in the brackets repeat infinitely.

Rick DeNatale

Yeah I think they would be better off with rationals

On 06/05/2009, at 1:30 PM, Rick DeNatale [email protected]

Rick Denatale wrote:

On Tue, May 5, 2009 at 9:01 PM, Samuel L. [email protected] wrote:

Can anyone offer an explanation?

BigDecimal is still a kind of float, albeit a decimal float rather
than a binary float.

Many thanks Nobuyoshi and Rick, that makes complete sense now.

I guess the safest rule of thumb is if you’re doing comparisons for
humans, use humanized numbers (i.e. integers

Cheers, sam

2009/5/6 Samuel L. [email protected]:

Many thanks Nobuyoshi and Rick, that makes complete sense now.

I guess the safest rule of thumb is if you’re doing comparisons for
humans, use humanized numbers (i.e. integers

Or define a maximum error, i.e. do not rely on identical values but
rather the difference of the quotient.

Kind regards

robert