For about the last week I have been seeing the number 13 in one way or another. I mean everything lately seems to be 13 something. Am I in for trouble?

 
+13

It's just a Bakers Dz., and besides, you should only worry if you're superstitous.

I had a similar thing many years ago when the number 22 kept cropping up everywhere. I was 22 at the time. I kept waking up and looking at my clock and it would be 22 minutes past the hour. Then one day a small piece of paper came through my letterbox with the number 22 printed on it. Having said that, I took a fair bit of acid in those days. I think it was a drug-induced mix of OCD and psychosis. 

I was stalked by an irrational number once.  When asked why it was following me, it wasn't able to give a logical reason. 

Good luck this Sunday.

Yes, both numbers are significant and you can say that 13 has two significant figures.
 
It becomes a bit trickier with a number like 10 or 100 (i.e., when zeros are involved).  For example, the number 100 has one significant figure but if you wrote 100. then you have three significant figures with the decimal point indicating that the zeros are significant.
 
Additionally, if you have the number 100 and you know that only two of the numbers are significant, then you would use scientific notation and write 1.0 x 10^2.  That gives you 100 to two significant figures.
 
Hope that helps.

"...And now, we're going to play a little imaginary number for your listening pleasure!"

Starise has not been heard of since this ominous post. 
 
If you are in strife with nubmers, flip to a different base , eg base8

I also believe that license plates have hidden messages in them.