There are 3413 btu per kWh and 100,000 btu per therm of natural gas, these are constants. In order to give a correct answer the exact efficiency rating of the high efficiency furnace and the energy costs per kWh and therms would need to be known.
Friction.
Lennox top o the line furnace is 98.2 percent efficient
friction and other environmental forces ar responsible for <100 % efficiencies of machines.
furnace highest rating is 97 % efficient for a residential model. This is known as a condensing furnace.
100 %
nothing has 100% efficiency.
Perhaps an electrical AC transformer can have 99 percent efficiency. A loudspeaker can have only 1 percent efficiency.
99.4%
it is the amount of work that can be done. a machine can use 300,000 J of energy but it only uses 263,000 J. that is percent efficiency.
watches
The laws of thermodynamics imply that there will always be some loss of efficiency.
It is not a good efficiency engine.