significant figure representation? I was wondering: 
Why does
$1.30 \times 10^3$ have $3$ significant figures
while $1300$ has $2$ significant figures
(they are both the same number)
Why is that distinction ?
When should I use each ? 
 A: I found the following sentence in  http://en.wikipedia.org/wiki/Significant_figures
"In particular, the potential ambiguity about the significance of trailing zeros is eliminated. For example, 1300 to four significant figures is written as 1.300×10^3, while 1300 to two significant figures is written as 1.3×10^3".  
This is the problem of trailing zeros. In Wiki page, the expalnations are quite clear on this topic.
A: If you write $1.30\times 10^2$ instead of $1.3\times10^2$, some people construe that to mean you're claiming it's accurate to the nearest $0.01\times 10^2$.
I.e. "$1.30\times10^2$ means $(1.30\pm\text{half of }0.01)\times10^2$, whereas $1.3\times10^2$ means $(1.3\pm\text{half of }0.1)\times 10^2$.
In one case you're rounding to the nearest $0.01\times10^2$, and in the other to the nearest $0.1\times10^2$.
It's just a matter of how much accuracy is being claimed.
A: That is what I was taught, but I don't think it is universal.  The difference is in approximate numbers.  $1.30 \times 10^3$ represents $(1.30 \pm 0.0005) \times 10^3$, while $1300$ could represent $1300\pm 50$ as any number in that range would round (using 2 SF) to $1300$.  In the case of $1.30 \times 10^3$ the writer went to the extra trouble to write the trailing zero.  In the case of $1300$ we don't know how many of the zeros are significant.  I was also taught that when I cared and had 3 SF, I should write it $13\underline 00$, but I haven't seen that since.  If you really care, you should use $\pm$ the error bound.
