Can someone more familiar with $BITC explain how Bitcoins can be portioned? I get that each bitcoin is a unique number - how can 0.4 of a number belong to someone and the other 0.6 of that number belong to someone else?
There are really no "Bitcoins", there are only a very long series of inputs and outputs to various Bitcoin addresses, all recorded on the shared block chain. Inputs (Bitcoins) come in to the system through mining, and then they are traded out via outputs and in via inputs.
The smallest value for an input/output is 1 Satoshi. 1 Bitcoin equals 100,000,000 Satoshi. So a Bitcoin is just a convenient measurement of inputs minus outputs.
When you make a purchase from an address, the client adds up your inputs and outputs at that address, and if you have a positive balance, you can send any portion of it as an output to another address (as long as you have the private key to verify that you own the sending address). It is recorded on the block chain as an input to that receiving address records, and the miners (eventually) confirm that transaction by including it in a block -- each time that happens is 1 confirmation (mining is another whole can of worms).
When you make a purchase that is less than the total number of inputs minus outputs at the address you're spending from, you can receive the difference via an input to either the same address or another, new address, depending on the Bitcoin client used.
Does that make sense? It's all just a shared accounting system.
Bitcoin transactions have a fundamental unit which is much smaller than a whole bitcoin. Actually it's 1/100,000,000 XBT! These tiny units are called satoshis, after the creator of the bitcoin protocol.
A bitcoin doesn't have a unique number at all. The unique number that you are thinking of is effectively an "account id". When bitcoins are mined, essentially a ledger gets created saying that "account id" #1234567343533 has 25.000000000 bitcoins in it. When you send someone money, you say "from #1234567343533, send 0.05000000 BTC to #111111111, and 24.95000000 BTC to #1234567343533"
The same way that you can send someone part of a dollar. The atomic unit of USD isn't the dollar, it's the cent (setting aside some financial instruments). Likewise, the atomic unit of BTC isn't a bitcoin, it's a satoshi (1 * 10^-8 bitcoin).
The unique number that you're thinking of isn't the bitcoin itself, it's the proof that that value was yours to spend.
