Praise be to Allah.
The value of the nisab [the amount that determines whether zakah is obligatory; anyone who has more than this is obliged to pay zakah] for dollars or other currencies is whatever is equivalent to the value of 20 mithqals [a unit of measurement] of gold or 140 mithqals of silver at the time when the zakah 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. (Fatawa al-Lajnah al-Daimah, 9/257) and because this will be more beneficial to the poor. (Fatawa al-Lajnah al-Daimah, 9/254)
Given that currently the price of silver is lower than the price of gold, the nisab should be based on the price of silver, so if a person’s wealth (in paper money) reaches the nisab on that basis, he has to pay zakah.
The nisab 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 Allah knows best.