Which number is more precise?

The precision of 10000 and 125000 is ambiguous. It is unclear whether 10000, for example, is precise to 5 figures and it just happens that the value is 10000 or if it is precise to 1 figure and the zeroes are place holders. Or it could be precise to 2, 3 or 4 figures. In these cases, the author may specify what digits are significant with underlines or bars or some other convention (which I gave never actually seen). More commonly (at least in what I've seen), the number will be written in scientific notation, which is unambiguous. Here's another way to look at: 10000 is equal to 1.0*10^4. It is also equal to 1.00*10^4. The former has 2 significant figures while the latter has 3. Which is correct? With the available information this question is impossible to answer, hence the ambiguity.

The precision of 15 versus 7 is more clear cut. 15 has 2 significant figures while 7 has 1. Thus 15 is more precise than 7. With that said, the context of whole numbers is important in calculations. Whole numbers that aren't empirical (ie that are not obtained from measurements) have unlimited significant figures. For example, you have 7 weights that each have a mass of 1.00 grams. Would the total weight be reported as 14.0 grams or 1*10^1 grams (that's 14.0 to one significant figure). The answer is 14.0 grams.

The more significant digits a number had, the more precise it is. So, in your first example, 10,000 has one significant digit while 12,500 has three significant digits. 10,000 can be rewritten as 1x10^4 and still have the same information. Rewriting the second value in scientific notation gives 1.25x10^4. You need three digits to give the same amount if information. Basically, rewrite the number in scientific notation. However many digits it takes will be the significant figures. Here are a few more examples: 10 - 1 sig fig, 10.0 - 3 sig figs, 15 - 2 sig figs, 7 - 1 sig fig. Hope this helps.