What is the ruling on exchanging torn banknotes that are not accepted for circulation for half their value in some banks?

The rule for exchanging gold for gold and silver for silver is equality, and there is no difference between flawed, broken, or other types. Banknotes serve the purpose of gold and silver as a price for things, but not all rulings applicable to gold and silver can be applied to them due to their lack of intrinsic value. Therefore, there is no impediment to exchanging a torn banknote for half its value, as it has lost its [full] value.