Bitcoins are over $800, I need to pay someone about $200. Is it possible to pay someone with a partial bitcoin?
Yes! To send $200 at a Bitcoin price of $800/BTC, you'd send 0.25 BTC. Bitcoins are highly divisible, up to eight decimals behind the point. The smallest subunit of a bitcoin is currently still less than 1/1000 of a cent.
Many Bitcoin clients will also keep track of the current value of Bitcoin and allow you to enter the amount of a payment either as bitcoins or your preferred national currency.
For example, when I want to send someone $5 from my phone, I could either enter BTC 0.00625, or $5 to set the amount.
As Bitcoin has become so valuable that one bitcoin is worth much more than many things we want to pay for, some people have moved to denominating prices in mBTC, i.e. millibitcoin, which are 1/1000 of a bitcoin.