Are the banknotes that we deal with forbidden, because they do not represent gold or something of value?

Money is of two types: natural, like the gold dinar and the silver dirham, and conventional, like the fulus (copper coins) and paper money. Dealing with paper money was known anciently, and Imam Malik alluded to the possibility of taking paper as money. It is not a condition for currency to be made of gold or silver; rather, the matter depends on its circulation among people and its acceptance as a price for things.