I have been curious for quite some time, if the calculation of the US National Debt is the quantity with the most significant figures that’s regularly used. It’s currently at 16 digits, and is calculated each and every business day. Their FAQ states that “daily accounting is still the most effective, efficient, and accurate way to account for the debt.”
Most physics constants don’t have anywhere close to 16 digits of certainty.
Insert obligatory reference to Feynman’s quote on economical numbers here.