Why does 0.00 have zero significant figures and why throw out the implied precision?

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Per the accepted answer here:

How many significant figures in 0.0

Supposedly, a value like 0.00 has no significant figures. However the implication of that measurement is that the true value could actually be something like .0005, we just can't measure it. But we do know, for example, that it's not ".1".

If we were to take that value and multiply it against another measurement the result would obviously be zero, and with zero significant figures it would seemingly be correct to report the result as simply "0" - because it's bad practice to report more significant figures than necessary (correct?). But that doesn't convey anything about the true precision or accuracy of the measurement. A value of "0" doesn't tell the reader that we actually do know that the value is < 0.1. Would we not want to report it as 0.00? And if so, why wouldn't we also say that it has 2 significant figures?

In other words, saying something has zero significant figures seems to throw out valuable information. What is the downside of handling 0 as an edge case.

FWIW - I have seen other sources explicitly say that zero values should be treated differently, but I consider those to be less reliable than this site.

Edit:

As for how I imagine handling it, it seems 0 values would be an edge case where scientific notation may sometimes be required? e.g. The measurement 0.00010 has 2 sigfigs (or in SN, 1.0e-4). A measurement with the same apparatus that reports 0.00000 should seemingly also have at least 2, but we cant determine that from the string. When ambiguous perhaps it must be written as 0.0e-4 or 0.00e-3 depending on the edge case convention? I realize the exponent is arithmetically irrelevant for the value 0, but it seems like there should be a way to convey both the precision and the uncertainty?

Just spit balling. I may be wrong about everything here!

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The answer in the cited question say the right thing if you measured to 0,00 0,005 is not excluded than that is your error not 0,00 or if you know it better maybe 0,001?