The ISS needs about 7 tons of fuel per year to hold orbit. I just tried to calculate the air density in the 400 km orbit with the scale height 8.5 km.
Air density there should be $\frac{1}{e^\frac{400}{8.5}} $compared to the sea level. But this seems far too thin, because at this calculated air density there would be too little air to cause 7 tons fuel usage to hold orbit.
In the mean time: Scale height depends in temperature. So above 100 km, use 24 km instead of 8,5 km. So I repeated the calculation with scale height 8,5 up to 100 km and scale height 24 from 100 to 420 km. This I multiplied with 7691 m/sec, 86400 sec a day, 365 days a year gives about 3. The result means 1 m² ISS hits each year as much air as 3 m³ at sea level. This matches good the fuel usage to hold orbit.
