Change the line

for rec in constants[:-10]:

to:

for rec in constants[constants['rel_unc'] > 0][:10]:

and the format specifier in the output line to ':g' (since the uncertainties are less than 1 ppm).

1.79792e-07 ppm: electron g factor = -2.00232
1.79792e-07 ppm: electron mag. mom. to Bohr magneton ratio = -1.00116
1.06719e-06 ppm: kilogram-hartree relationship = 2.06149e+34 E_h
1.07488e-06 ppm: atomic unit of time = 2.41888e-17 s
1.07672e-06 ppm: hartree-kelvin relationship = 315775 K
1.08702e-06 ppm: atomic unit of current = 0.00662362 A
1.08846e-06 ppm: electron volt-hartree relationship = 0.0367493 E_h
1.08994e-06 ppm: joule-hartree relationship = 2.29371e+17 E_h
1.09259e-06 ppm: hartree-kilogram relationship = 4.85087e-35 kg
1.09352e-06 ppm: Rydberg constant = 1.09737e+07 m^-1

The most accurately known constant is the electron $g$-factor.