So if I have a $100 bill and I snip off just 000000000000000000000000000000000000000000000000000000000000000000000001 % of the $100 bill, is it no longer worth $100?

That's different. If you cut off 40% of the bill, stores will still receive the money.
as long as 50.6% of the bill is there, they have to take it. If it's cut exactly in half, then the money is not eligible for purchasing items.

I was always told that if the unique ID number on the bill is on the bill that you give to the recipient, then the bill is legit.

Refer to Kahl4Prez's signature.

Yeah, for a legit bill, it has to have at least 50.6% of the bill remaining (meaning only 1 half can be used. You can't cut it in half and have 2 100$ bills), and the correct ID #. It cannot
be counterfeit.

How can you measure 50.6% exactly if somebody just gives you $100 bill from out of the blue?

Lol, well, most people will just assume it's exactly half because they're so similar in size, so they discard it. Unless you pull out a ruler and measure the whole thing and then the 50.6% part of it they'll most likely discard it.
Most of the time, people will just hold 1 part of the bill over the other part. If they're the same size, then they won't take it. If another part is bigger than the one part, then they'll take the bigger part and throw away the smaller.
But this doesn't happen often as people are usually very careful w/ their hundred dollar bills

.999999 will never equal 1.
It's as simple as that. Stop with all of your bullshit.

That's what I'm saying

Wrong on (almost) every point.

.999... is a number. Thus it cannot 'get closer and closer and closer' to 1. Numbers don't get closer to other numbers. Numbers don't move. [Functions and sequences can be described as getting closer and closer.]

So you understand that there is no number between 1 and .999... Good. That is both a necessary and sufficient condition for two numbers being EQUAL. The SAME. [Not "next to each other." That makes no sense. They either are the same or aren't. Being "next to each other" means there is some distance between them - and hence different numbers. This is not the case for 1 and 0.999...]
In fact, a satisfactorily rigorous mathematic proof that .999... = 1 would be *precisely* to show that the distance between the two numbers is zero.

There's no rounding going on anywhere at all. None.
Try to back up what you say with some arguments next time and I'll gladly show you how you're wrong again.

there is no interger number between 3 and 4, does that mean they are equal intergers?