Leading zeros are not considered significant figures when they are placeholders used to express the magnitude of a measure, in cases where the magnitude itself is considered essentially certain.
For instance, if you say that the diameter of a €1 coin is 0.0232 metres, it’s clear that the leading zeros are placeholders, since it was already obvious that the diameter of a €1 coin is less than 0.1 metres. In information-theoretic terms, the leading zeros don’t convey any bit of information.
On the other hand, when you are dealing with estimates where there is uncertainty even on the magnitude, then the leading zeros are significant: If you say that the probability of an event is 0.0005, and it wasn’t already obvious that it was less than 0.001, then the leading zeros do convey information.
Any probability greater than zero can be expressed as a fraction of one: p = 0.0005 = 1/2000, thus transforming leading zeros into trailing zeros, which may be significant figures depending on the case.
Note that, on the other hand, the inverse of physical quantity (other than time/frequency) is not generally an intrinsically meaningful number.
Leading zeros are not considered significant figures when they are placeholders used to express the magnitude of a measure, in cases where the magnitude itself is considered essentially certain.
For instance, if you say that the diameter of a €1 coin is 0.0232 metres, it’s clear that the leading zeros are placeholders, since it was already obvious that the diameter of a €1 coin is less than 0.1 metres. In information-theoretic terms, the leading zeros don’t convey any bit of information.
On the other hand, when you are dealing with estimates where there is uncertainty even on the magnitude, then the leading zeros are significant: If you say that the probability of an event is 0.0005, and it wasn’t already obvious that it was less than 0.001, then the leading zeros do convey information.
They convey information, but they are not significant figures, which is a term with a specific meaning.
Well, if you have to nitpick...
Any probability greater than zero can be expressed as a fraction of one: p = 0.0005 = 1/2000, thus transforming leading zeros into trailing zeros, which may be significant figures depending on the case.
Note that, on the other hand, the inverse of physical quantity (other than time/frequency) is not generally an intrinsically meaningful number.