>But is keeping precision to the 15th place in the case of an energy density justified?

It's clear from the context ("This is still an approximation but...") that I do not imply such a precision.
I kept the decimals in order to make it faster visible that this is the outcome from an automated calculation involving thousands of measurements. And in some sense I wanted that people stumble over the decimals in order to have a more in-depth look at the whole thing. Moreover the whole thread started out with asking for more measurements. That is the 1W/m^2 could be easily due to a measurement error.