Why $0$ in number $50$ is not a significant digit? I have been reading definitions of significant figures which vary from source to source. 

1-The digits in a number that indicate the accuracy of the number are called significant figures or digits---College Algebra by Raymond A. Barnett and Micheal R Ziegler
2-Significant figures by definition are the reliable digits in a number that are known with certainty---Textbook of Chemistry by Prof Muhammad Omar Mangrio
3-The digits which give us idea of quantity and accuracy are significant digits---An Introduction to Error Analysis by John R. Taylor.
4-The significant figures of a number are those digits that carry meaning contributing to its precision---Wikipedia (somewhat close to definition 1)

A rule for determining significant figures in a number is that, Zeros that locate the decimal point in numbers larger than one are not necessarily significant. For instance the number $1570$ has only $3$ significant digits $1,5$ and $7$
I can't figure out that how this rule is consistent with the definitions above. Or simply my question is why $0$ in the number $50$ or $15700$ is not considered to be significant?
Whenever I asked my teacher, he said that zero is not for the purpose of indicating accuracy here. I didn't get him! Any helpful example related to measurements would be greatly valued.
 A: I would say that 50 could be to either 1 or 2 significant figures, depending on the context or calculations (etc) of the author (or measurer) of the number. Similarly, 15700 could be 3, 4 or 5 significant figures. For example, a scientist may report in a paper that he/she has measured the length of an object to be $50m$, to 1 significant figure (making the lower and upper bounds $45m$ and $55m$ respectively), but they may also report instead that the measurement was to 2 significant figures, making the bounds $49.5m$-$50.5m$. Another way this author might express the same thing is to use "plus-minus"; the first would be something like $L=50\pm5 m$, while the second would be $L=50\pm0.5 m$.
If I say "this object is 50m long, to 2 sig.figs." then that is more precise, but just as valid, as saying "this object is 50m long, to 1 sig. fig."
A: I'm not sure, but if you want it to be clear that you mean 50 more specifically than just "approximately 50", you can write 50. with the period after, then I believe 0 is considered a significant digit
A: Suppose I have a meter stick with no markings on it. I round my height to the nearest meter. I say "I am 2 meters tall, to the best accuracy I could find with my equipment." This is not very precise. I could be 151 cm tall. I could be 249 cm tall. You don't know.
Now, a meter is 100 centimeters. So, using my equipment, I could say, "I am 200 centimeters tall, to the best accuracy I could find with my equipment." But just because I changed the units, doesn't mean that my measurement was any more precise. I made the measurement with the same stick and I rounded in the same way. The only difference is the way I expressed it. We see that the 0's at the end of the number are arbitrary; an artifact of what unit we wish to use. The only thing real is the "2" and there is one significant figure.
A: To my understanding,"Significance" for mathematics should mean the number have value.For example $0.305$ as a number.The first "0" is not significant because it have a value of "0",but second "0" have significance because it had a value of 0.30.
It is very unclear of what "significance" means because it's definition is not universal.To me,the 0 in $50$ is significant because it holds a digit of "50".It does have a value,a quantity.
