Nice to see someone using LOGs. But I would trust your results more if you displayed them, instead of using the WHERE expected_result <> actual_result.

The problem I found was that you don't get exact representation when using float. Frankly, I have never used float before, so maybe I am doing something incorrectly, but note the example below.

declare   @num float

           , @res float

           , @digits int

SET @num = 1.23456678

SET @digits = 4

select @res = case when @num > 0

                      then round(@num,@digits-1-floor(log10(@num)))

                      else round(@num,@digits-1-floor(log10(-@num)))

                    end

select @num as ORIGINAL_NUMBER, @res AS RESULT 

       , @digits as NBR_SIG_DIGITS

RESULT IS:

ORIGINAL_NUMBER         RESULT                  NBR_SIG_DIGITS

1.23456678             1.2349999999999999            4

Probably not what you really want (I assume you want 1.235 ??)