The general consensus on the wording you are referring to (in Biocompatibility) is that the "round down to the nearest tenth" is referring to the multiplier, not the final essence cost.
As you pointed out, there are many essence costs that will quickly fall below one tenth of an essence point, and this quality would seemingly reduce these essence costs to zero, and that is not likely the intent. If you instead treat the biocompatibility as a modifier to the essence cost multiplier, it works out better. The example Biocompatibility gives actually uses that, the .72 rounded down to .7 is talking about the cost multiplier for Alphaware grade cyberware.
This rebate is cumulative with the reduction offered by the chosen 'ware's grade, if any (e.g., the reduction for alphaware of 0.8 is reduced by ten percent, or 0.08, to become 0.72, and is rounded down to 0.7).
GRADE | ESS COST MULT. | ESS COST MULT W/ BIOCOMPAT. |
Standard | x 1.0 | x 0.9 |
Alphaware | x 0.8 | x 0.7 |
Betaware | x 0.7 | x 0.6 |
Deltaware | x 0.5 | x 0.4 |
Used | x 1.25 | x 1.1 |
Except cranial bombs