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The most precise measurement I know of is the frequency of a laser-cooled Rb 87 standard 6,834,682,610.904333 which is handled with full precision by 64-bit floating point.

If you think this isn't precise enough for you, maybe you don't really understand your precision needs.

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Or you aren’t doing something physical. For example there are tons of things in math that can use as much precision as you want. For a toy example, looking at rates of convergence or divergence in extremely small regions of the Mandelbrot set. There are techniques that cut down the requirement for precision for that problem, but they are necessary because the default level of precision is insufficient.

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