How are fractions of bitcoin implemented and spent? If the ability to spend bitcoins and therefore bitcoins depend on/correspond to private keys, how can fractions of coins exist? Can the key be split up? How are fractional transactions signed versus integer transactions? I am not asking what the subdivisions of bitcoin are or how it can be further subdivided.
Bitcoin doesn't use the concept of "balances" it uses transactions.  A transaction consists of inputs and outputs.

The transaction amount is the total of all inputs.  Each input in a transaction is spent in its entirety during the transaction.   And the outputs can total any amount up to the total transaction amount.  Any amount remaining (inputs - outputs) goes to the miner as a fee.

So a transaction might look like:

INPUTS:
25 BTC
50 BTC

OUTPUTS
40.2 BTC
34.7 BTC


So the 75 BTC total inputs, less 74.9 BTC total outputs means 0.1 BTC goes to the miner.

Now, at the protocol level, the 25 BTC amount is really 2,500,000,000 because each 1 BTC is actually 100,000,000 Satoshis.   

So the 34.7 BTC output was really the number 3,470,000,000.

So there are no fractions.  These are all integers.

When the client displays these numbers, it shows them in whatever units the client is configured to use (BTC, mBTC, uBTC).