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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!

The Shoe Shiner
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1 Answers1

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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?

trula
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  • How would you know that 0.005 is not excluded from the value "0"? In fact how would you know that any value is excluded? The uncertainty might be extremely high. The true value could be 10 million. You have no way of knowing. And according to that answer,"0" is a perfectly valid representation, because 0.00 has no sigfigs. – The Shoe Shiner Aug 10 '23 at 14:25
  • I don' understand. If you measure something for example a mass or a length, you have to know how exact your measurement is. if your measurement is 0,00g and not 0.000g you imply it could be ±0,005 otherwise you would give more exact values. So you have to say, what you mean with m=0,00g probably that your scale or measuring instrument can not measure 0,001g? – trula Aug 10 '23 at 17:29
  • 0.00g means the apparatus can only measure to the hundredths place. That it is the limit of its precision. But according to significant figure rules, 0.00 can be written as "0". Which makes no sense to me. – The Shoe Shiner Aug 10 '23 at 20:01
  • This means you have m=0±0,005 g what you should write and not m=0,00 g but writing m=0,00±0,005 is not wrong – trula Aug 10 '23 at 22:17
  • I don't think you should write that unless you actually know it. – The Shoe Shiner Aug 14 '23 at 11:34
  • Because there is such a thing as "implied uncertainty" , and that's basically what Im referring to here. – The Shoe Shiner Aug 14 '23 at 11:48
  • I stop here, but don't understand you if your scale can only measure up to 0.00 you have ti admit of a possible error of 0,005. if you know more you can also have 0,00±0,002 so what is the "implied uncertainty" – trula Aug 14 '23 at 14:21
  • Im saying you dont have to write the uncertainty. You should be able to write 0.00 and the uncertainty is implied. And when you write 0.00 you run into the significant figures problem which is the core of my question. – The Shoe Shiner Aug 14 '23 at 15:57