76.5 hours
Reasonable load range: 38.2 hours to 128 hours
Calculation
9,000Wh × 85% usable efficiency ÷ (100W × 100% duty cycle) = 76.50 hours.
What can change the result
Actual device wattage, battery age, ambient temperature, inverter standby draw, conversion losses, power-factor behavior and cycling frequency can all reduce or extend runtime.
Check output before connecting
The battery or UPS needs at least 200W continuous capability and about 250W surge capability. Watt-hours alone do not prove compatibility.