Everyone knows that in space, every gram counts. Knowing how much mass an orbital object has is necessary for precise motion calculations.
So how precisely do we know the mass of ISS? I'm sure we can estimate it's weight to a few dozen kilograms. But there is lots of stuff going in and out and stuff might even be leaking a little. How much effort is put into bookkeeping ISS's mass? To clarify, I'm talking about everything that is on or inside ISS at this moment, including people, cargo or connected spacecraft.
And what precision is needed to keep ISS running? If we weren't able to achieve that precision, what problems would there be in running ISS?