The Force Quit Fallacy
The only time you need to force-quit an app is if it is frozen, or otherwise misbehaving — beyond that the best battery life can be attained by not force-quitting any apps.
Update (2016-03-10): Mitchel Broussard:
Asked specifically whether Cook quits apps to save battery and if it’s truly “necessary for battery life,” Federighi jumped in with a concise “no and no.” Although far from an official condemnation of the force quit belief by Apple, it is the most the company has directly said about the myth in the six years since multitasking became available in iOS 4.
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