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Since the speed of light (in a vacuum) is a constant, its number of significant figures should be infinite, right?

But if I were to say that the speed of light $= 3\times10^8$, would the number of significant figure be $1$?
Or, if I were to say that the speed of light $= 3.00\times 10^8$, the number of significant figures would be 3 now?

In general, if someone asks me “How many significant figures does the speed of light have?” what is the answer? Will it be different considering whether the value is specified or not? This is not about uncertainty but about how many significant figures does it have in general? Like if i were to just say 'c' so would it's significant figures be counted or not? If yes, then how many?

Hani
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3 Answers3

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The meter and the second are defined to be the units of time such that $c = 299792458$ m/s exactly. This number can be thought of as having an infinite number of significant figures, since it is an exact integer.

However, if you round the speed of light off to include fewer digits than this, then it is no longer exactly precise. That means that in calculations, you should treat it as though it has as many significant digits as you used when you did the calculation. So if you used $3.00 \times 10^8$ m/s, your final answer would be found by assuming that your value of $c$ has 3 significant figures and round your final answer accordingly. If you used $2.9979 \times 10^8$ m/s in your calculations, then you would have to assume that your value of $c$ has 5 significant figures. And so forth.

Michael Seifert
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Physical quantities don't have significant figures. Measurements have significant figures. If you perform a measurement of the speed of light, and you're confident that the first five digits of your measurement are informative, then that measurement has five significant figures, and when you report the value you got, that will have five significant figures. Significant figures are about your level of certainty, not about the physical thing you're measuring. If you say "speed of light=3.00×10^8", you're saying "I'm confident that the speed of light is around 3.00x10^8, with the error being less than 10^7." That's a statement about the error of your measurement, not about the speed of light itself. You're using the sequence of symbols "3.00×10^8" to represent the speed of light along with how precise you think you are, and it's that representation that has significant figures. Have you seen graphs where a value will be represented by a point plus error bars? It's the same idea; those error bars represent a certain number of significant figures. It's the "point plus error bars" that has the significant figures, not the thing being measured.

Acccumulation
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If you use Planck Units the problem dissolves. The speed of light is 1. Not 1.0, not 1.00000, but just 1.

Simon Crase
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