I would simply walk up to them, say "I think you dropped this". Hand it to them and walk away without expectations of a reward or even a "thank you". To me, just making someone happy is reward enough.
On the other hand, there may be reasons why I might keep it. Hypothetically if I really needed the money or if it was some person that deserves to go without it like a drug dealer.
How do you know its theirs? How do you know they haven't dropped something else and are looking for that. If I physically saw them drop the note then I would. I actually did find a wallet, away from security cameras in my university library which had £100 in. I could have simply taken it, however I handed the wallet into reception and they contacted him as his student ID was in it. Ironically both the ladies at reception looked amazed that I was honest enough to hand it in. And when the guy did receive his wallet, he claimed there was more than £100 in it and accused me of stealing from him! A disgrace. But to answer the initial question if I was certain it belonged to them then yes I would give it to them.
You see if 100 dollars can be enough to help a home less person he back on his feet then 100 $ is enough to change any thing, even a persons life. . . And can change the world completely, in my conclusion yes i would give it back .
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I don't think that my subconscious would let me sleep at night with the feeling of a bad decision in the back of my head. I would probably stop and think for a sec but after-all I would give it back to the owner. This is also called being a human. If this would happen to you, you would want the founder to give it back to you, so you should do the same.
I will return it to the person. I am a honest person. This money isn't money, so why should I take it? Also, the owner of this money might need this money for important use. I shouldn't cause stress on him over money. Plus, I am good enough to survive so i don't need that money
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If i found 100 bucks and knew whose it was i would give it back to them because its the right thing to do. If i lost 100 dollars i would want it returned to me. Treat others how you want to be treated. I would return it to them.
If it was someone I personally knew or someone I would like to know then I'd probably give the money to them as it would be in my best interest to. However if it was a stranger or a person I didn't like then of course I'd take it and not say anything about it. I'm a scavenger at heart and my own happiness/pleasure goes over others in the scale of priority.