How is the monetary part of bitcoin stored?
Within the Bitcoin protocol, each Bitcoin is represented as 100000000 satoshis. Therefore, you can divide bitcoin up with a precision of 0.00000001.

In a transaction, the number of satoshis being delivered to each output is recorded, along with a record of which previous output is being spent.

The fee is then derived from sum(Inputs) - sum(Outputs). The actual representation of the amount itself is encoded using the Variable Length Integer representation