The value of the money is formed individually and expressed in the market. Basically each actor compares two things at the time and decides what is best for him at that moment. A nickel or a coke. Maybe you (mirelo) confuse it with the unit of account. That is something that is chosen by a businessman, and the crucial traits are fungibility and divisibility.
The value of money is not "formed individually," but socially. It is not just "expressed in the market," but decided by the market. No buyer can determine the price of anything independently of the seller.
By the way, a 10 dollar bill is not exactly as valuable as 10 one dollar bills, that you will discover, if you go to a bank with truckloads of money, they will charge you for handling the notes.
You forgot to mention they can only charge you using the original monetary unit, the value of which is hence unaffected.