Businesses in town are almost fanatical about change. I almost started an international incident trying to pay for a 5.25 gryvna bottle of water with a 10 gryvna note. Salespeople and cashiers will almost always ask you if you have the change (kopecks) for whatever your price is.
Even though 100 gryvna is about $20, don't expect to be able to use it at any street vendor. Best bet is to get smaller bills at a bank or break it at your next restaurant stop.
If someone comes up to you on the street and doesn't look to be selling anything (nor do they look drunk), listen carefully to what they're saying. If one of the words you hear is "chas", they're asking you what time it is. On the other hand, giving people the time would be a great way to make an exit if you were accosted by someone drunk or selling something, I suppose.