Okay class, here is a simple radiant physic problem.
You have four layers. layer 1, emissivity = 0.9965, layer 2, emissivity = 0.8570, layer 3, emissivity equals 0.7091, and layer 4, emissivity = 0.6092 Calculate the flux from layer 1 at 390Wm-2. to layer 4. Now do the same thing with only 2 significant digits. How's that confidence in your theory hanging in there?
Two significant digits instead of 4 is half the warming.