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So I know all the significant figures rules, but an edge case that doesn't quite make sense to me is 0. Say I measured the mass of an object to 0.000g. How many significant figures is that measurement to? As close as I can tell, it would be 0 significant figures by the rules I know, but it doesn't make sense that a measurement that precise would have no significant figures.

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Although there are explicit rules for counting significant figures, they are really a rough idea for the accuracy of a number. You have shown that the mass is less than $0.000\ 5$ gram, but it could be $0.000\ 000\ 005$ gram for all you know. In the sense that one significant figure indicates that you know the value to about $\pm 10\%$ (it ranges from $5\%$ if the figure is $9$ to $50\%$ if the figure is $1$), it makes sense to say you have no significant figures at all because you have no bound on the fractional error that might be made.

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    $\begingroup$ The point being that significant figures have to do with relative error rather than absolute error. If the true value is $0$, the relative error is undefined. If the true value is nonzero, the relative error is $-1$. $\endgroup$ Feb 17, 2017 at 21:44
  • $\begingroup$ This should probably be the accepted answer. $\endgroup$
    – SapereAude
    Apr 5 at 20:13
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Zero significant figures.

Suppose your scale could weigh some mote of dust as $1\mu g$, and it has $0.5\mu g$ precision. Then you would say the measurement is $1 \times 10^{-6} g$, which is one significant figure. Anything below that wouldn't be effectively measurable. So you don't get any significant figures from a zero measure.

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If you write a number that is between 0 and 1, calculate how many significant figures it has. Then delete the last digit and there is one less significant figure. If you keep deleting the last digit until only zeros remain, there will be zero significant figures.

Example:
$0.020356$ has 5 significant figures,
$0.02035$ has 4 significant figures,
$0.0203$ has 3 significant figures,
$0.020$ has 2 significant figures,
$0.02$ has 1 significant figure,
$0.0$ has 0 significant figures.

It will work with anything that is between 0 and 1. So $0.003725$ and $0.020080$ will work similarly.

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  • $\begingroup$ The 0 in front of 0.0 is significant in the case of 0. $\endgroup$
    – CL40
    Jan 22, 2022 at 9:30

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