167 hours
Reasonable load range: 111 hours to 333 hours
Calculation
9,800Wh × 85% usable efficiency ÷ (100W × 50% duty cycle) = 166.60 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 150W continuous capability and about 180W surge capability. Watt-hours alone do not prove compatibility.