In the "Effects of adding chemicals" in The Pool Calculator, what you are seeing is NOT a rounding error. It is instead taking into account the fact that the Trade % of 6% bleach is actually 6.17%. The 6% listed in the ingredients for bleach is a WEIGHT percentage of bleach, but for your simple formula you need a VOLUME percentage of Available Chlorine aka Trade %. There is also a WEIGHT percentage of Available Chlorine and that is also printed on the Clorox Regular bottle as 5.7%.

Chlorinating liquid almost always uses Trade % (i.e. volume % of Available Chlorine) even though I've seen this percentage listed in the ingredients. Yes, this is all very confusing, but The Pool Calculator assumes that bleach is specified using a % weight of sodium hypochlorite but for its calculations it uses the Trade %. For chlorinating liquid, it assumes the strength is already in Trade %. Now while The Pool Calculator does this correctly in the "Effects of adding chemicals" section, in the FC Now Target section it seems to incorrectly use Weight % for all bleach entries even when they are a high enough % (such as 10 or 12.5) to imply chlorinating liquid that is more likely a Trade %.

The formulas for these conversions are as follows:

Trade % = (Weight % NaOCl) * (Specific Gravity) * (Cl2 g/mole) / (NaOCl g/mole) = (Weight % NaOCl) * (Specific Gravity) * (70.9064) / (74.44) = (Weight % NaOCl) * (Specific Gravity) * 0.9525

Weight % Available Chlorine = (Trade %) / (Specific Gravity)

The density of 6% bleach is around 1.08 while for 12.5% chlorinating liquid it's around 1.16.

Yes, this is all very confusing, but fortunately it doesn't matter that much unless you are looking at better than 3% accuracy.