Molarity of water is about 55 Moles/liter so I am getting ~0.25 ppm.
Not sure what kind of ppm you are talking about, in most cases it would be just w/w. 1.3×10
-5 M means around 5.7×10
-4 g per L, or 0.57 mg/L, or 0.57 ppm (assuming 1L = 1kg of solution).
And let's not forget carbon dioxide is not an inert solute, it combines with water and dissociates, so its solubility is pH dependent. Typical freshwater aquarium will have a pH somewhere between 5 and 8 (well, perhaps I am slightly exaggerating), so it is around 3 pH units difference - and that means huge difference in the carbon dioxide solubility.