A touring bicycle's tire has a volume of about (1.0x10^-3) m. When inflated properly and thermally equilibrated, its pressure is about (6.810x10^5) N m^-2, as measured by a typical mechanic's pressure gauge.

How much greater is the inflated tire's mass than when its internal pressure is at equilibrium with the atmosphere at SATP? (Assume that air behaves ideally and its average molar mass is 29 g mol-1.)

Note: Your answer is assumed to be reduced to the highest power possible