How to Calculate with Uncertainty

“It is better to be roughly right than precisely wrong.”— Alan Greenspan While calculating with exact numbers is easy 4th grade math, scientific calculations with approximate measurement values require some special considerations. Here is how to do it roughly right. The correct notation Every physical quantity, such as the gravity constant1 $$\mathrm{G} \approx 6.674\,08(31) \cdot 10^{-11} \;\mathrm{m^{3}\,kg^{-1}\,s^{-2}}$$ should be correctly rounded, state the uncertainty, and specify the SI units using exponents.