How Accurate is Accurate Enough?

[Dave Shaffer]

(04-11-2021 01:15 PM)Chumango Wrote:  Are there real-life calculations where 10, 12, 14 digits are actually required? Or is it a matter of getting more digits and accuracy because we can? Just curious.

Yep!

I used to support a NASA geodesy program. That program is now measuring relative locations all over the earth to a millimeter or so (https://en.wikipedia.org/wiki/Internatio...ms_Service). In round numbers, the earth is about 12,740 km in diameter - 10^7 meters. So, 1 mm precision requires parts in 10^11 calculations. All our analysis programs used quadruple precision calculations.

These (NASA and other) systems use hydrogen maser time standards - we worry about stability here at parts in 10^15 - 10^16 (and can measure at that level!). And, current precision in atomic time keeping laboratory standards approaches parts in 10^18!! With such clocks, you can measure the effects of gravity on a clock by comparing clock rates at the bottom and top of tall buildings.