Praise be to Allah.
The value of the nisaab [the amount that determines whether zakaah is obligatory; anyone who has more than this is obliged to pay zakaah] for dollars or other currencies is whatever is equivalent to the value of 20 mithqaals [a unit of measurement] of gold or 140 mithqaals of silver at the time when the zakaah is owed. It should be based on whichever of the two works out better for the poor, because the prices of gold and silver vary from time to time and from country to country (Fataawa al-Lajnah al-Daa’imah, 9/257) and because this will be more beneficial to the poor. (Fataawa al-Lajnah al-Daa’imah, 9/254).
Given that currently the price of silver is lower than the price of gold, the nisaab should be based on the price of silver, so if a person’s wealth (in paper money) reaches the nisaab on that basis, he has to pay zakaah. The nisaab for silver is roughly equivalent to 595 grams of silver, so the one who has wealth has to pay 2.5% or 25 out of every 1,000 that he has in currency, after one year has passed). And Allaah knows best.