exact number having an infinite number of sigfig

[Seungri_Han_2J]

I read that exact numbers have an infinite number of significant figures. I am confused about this statement as to why this is true. Can someone please explain it to me?

[Chem_Mod]

Significant figures refer to precision. If you have a ruler that only has marks at inches, then you can be certain that your inch value is correct. Then, you can make an approximation for the tenths of inches, as you can make a pretty good guess if you have 1.2 inches or 1.8 inches. In this case, though, you can't say for certain that your tenths value is correct, because it was an approximation. This means your uncertainty is in your tenths place, and you can't make any approximations about hundredths of an inch with any sort of certainty. Thus, you have two sig figs.

However, if you have an exact number, there is no uncertainty. In a foot, there are 12 inches. This is a fact, and is by definition. So, if you convert feet to inches, you aren't uncertain, and you don't need to worry that uncertainty in the conversion factor is limiting the precision of your answer. This is why exact numbers have "infinite" sig figs.

[Olivia Fong 2k]

Hi! Exact numbers have infinite sigfigs because they are precisely a certain value (ex. constants in equations, such as 4 in 4*pi*r), so you can be certain they are exactly the value that they take. Thus, because they are wholly precise and there is no uncertainty involved, exact numbers can be thought of as having infinite sigfigs and shouldn't be used to determine the amount of sigfigs in a result. For example, if we're converting 51.4kg to kg, we know with certainty that 1kg = 1000g, so our final answer 51400g will have 3 sigfigs (because 51.4g has 3 sigfigs).

[angel oganesyan]

If I'm remembering correctly from high school, I'm pretty sure that because sig figs help with making uncertain values more certain for everybody, an infinite amount of sig figs can just be used as the entire number, as they have no uncertainty in their value. Therefore I don't believe sig figs count for exact numbers. Please correct me if I'm wrong tho. Essentially my reasoning and what I was taught is that numbers with a limitless precision don't need to have their significant figures considered. I hope this helps. :)