Counterfeiters never make one dollar bills, it's not worth their time. It is however possible to shrink paper money. i don't know how but i remember a kid in middle school doing it for the science fair, but his ended up being much smaller than that. I'd keep it.
P.S. $20 bills are the most counterfeit bills.
I'm not arguing statistics, since I know none, but in my personal experience, I've seen a higher quantity of counterfeit $5 and $10 bills than $20. My personal experience is from handling lots of cash at a pizza (delivery) place. Occasionally a driver will turn in a phony bill that they accepted, because it's hard to spot/check bills at night when it's dark, plus it's kinda rude to do that in front of the customer when they're hankering for a tip.
The counterfeit $5s I've seen are pretty awful. They've been small (but that's hard to notice unless it's with other bills) and the colors are all wrong. The $20s I've seen are fairly bad too, but nowhere near as bad as the $5s. The $10s I've seen are the most hard to spot (the new orange ones). The face side is pretty damn good; the colors are very close and hard to spot unless you've got a real one to compare to. The reverse side isn't nearly as good; the dark ink should be greenish, but the fake ones always come out with nearly black ink.
I've not seen a counterfeit $50, but I have come across a couple $100s. One was so obviously fake without even checking that I could only shake my head at the person who accepted it. Never mind that it didn't have a water mark or strip or shiny numbers. The other one should never have been accepted either, because it was only a week prior that we had that first fake $100, and I was telling people how to spot fakes. I told them how sometimes they would take a lower denomination bill like a $10, wash it clean of ink, then print a $50 or $100 on it. It'd still have the (wrong) water mark and the strip (in the wrong place), but people are unlikely to really look hard at the face - if it's there, then it's there. Sure enough, the second fake $100 was a washed $10 with Hamilton's watermark face looking at Ben Franklin.
I can usually spot a fake bill just by touch. Sometimes it's on paper that's obviously too thin/light, and when it's heavier/thicker, it doesn't have the right texture. But I handle thousands of bills a week.