Comparing two virtually identical BigDecimal numbers in Ruby on Rails

I got a little problem that I really would like to understand. I am using assert_equal to compare two BigDecimal numbers that are supposed to be identical. They actually are except a very little tiny fraction, see below:

-#<BigDecimal:7f4b40e8de78,'0.4021666666 6666666666 666666667E2',36(45)>
+#<BigDecimal:7f4b40e85db8,'0.4021666666 6666666666 6666668E2',36(63)>

I use assert_in_delta in order to not fail the test cases. So I got a reasonable workaround. I do wonder though whether it would be possible to have it equal:

assert_equal (241.30.to_d/6), model.division_function

The model's division_function does exactly the same. It divides a BigDecimal of value 241.3 by the length of an array, which is 6.

There seems to be a very tiny difference in the precision. I would like to know where that might come from? Is there a way I can control precision more accurately?

EDIT I am using Mongoid. It is worth to note that Mongoid offers BigDecimal as a field type, but it is stored as a string. However, I don't think this is the problem. I believe it is a Ruby thing.

EDIT I got a little further with an example which hints that it is a Ruby issue and not directly related to Rails. Please see below:

irb(main):041:0* amount1 = BigDecimal("241.3")
=> #<BigDecimal:7f49bcb03558,'0.2413E3',18(18)>
irb(main):042:0> amount2 = BigDecimal("1800")
=> #<BigDecimal:7f49bcaf3400,'0.18E4',9(18)>
irb(main):043:0> rate = amount1 / amount2
=> #<BigDecimal:7f49bcae8398,'0.1340555555 5555555555 5555556E0',27(45)>
irb(main):044:0> rate * amount2 #should return amount1 = 241.3, but it does not :-(
=> #<BigDecimal:7f49bcad6a30,'0.2413000000 0000000000 00000008E3',36(45)>
irb(main):045:0>

Solution

I reported the bug to the Ruby core team. However, this is not a bug as you can see in the rejection response.

BigDecimal, though offers arbitrary precision, cannot represent numbers like 1/3 precisely. Thus during some arithmetic you can encounter imprecisions.

You can use Rational in Ruby for exact numbers. Exercise caution when doing arithmetics if you wish to keep the result exact.