To start with, I am familiar with the rules that we have for sig-figs. I have two chemistry books by different authors (One by McMurry and the other one by Nivaldo J Tro).
I was doing some casual readig, I am familiar with sig-figs (or that's what I thought).
According to the first book, let's say I measure the thickness of the cover of a hardbound version of a book with a ruler that is accurate up to the nearest millimeter, and I find that it is 3±1 mm thick, or 0.3±0.1 cm thick. The book says I can claim just one significant figures when I use a ruler because it is accurate up to 0.1 cm, or 1 mm. The book clearly wants to say that I can't claim more than one sig fig if I use the ruler. For example, I can't say that the cover is about 3.2 mm thick, or 3.4 mm thick because the limitations of the ruler, it is not accurate up to 0.1 cm, or 1 mm. On the other hand, if I use an instrument that is accurate up to 0.01 mm (Vernier caliper, for example), I find that the book is 3.25±0.01 mm thick. It means I can claim three sig figs if I use a Vernier caliper because it is accurate up to 0.01 mm. Out of these three sig figs (3 2 5), 3 and 2 are certain digits and 5 is uncertain.
The other book, however, says that if I use a ruler (accurate up to the nearest mm) to measure the cover of the book, I can be sure the the cover is at least 3 mm thick, and then I can mentally divide the little space for a mm on the ruler into 10 parts and I can extrapolate that the cover is about 3.2 mm thick (or 3.3 mm, whatever). Now I can say that the cover is about 3.2 mm thick, out of which 3 is the certain digit and 2 is uncertain. That's what the book says.
In other words, there are two sig-figs according to the 2nd book, when we used a ruler to measure the thickness of the cover of a hardbound book. On the other hand, the first book says that we can claim only one sig-fig if we use the same ruler that is accurate up to the nearest mm.
I am confused, which one is correct? From what I understand about significant figures, I would think that the first book is correct in saying that we can't have two sig-figs if we use a ruler that can accurately measure up to the nearest mm. But the second book says that we can have two sig-figs.
Please help me with it