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Stuff just sitting in memory doesn't burn battery. Quite the contrary actually - loading/dumping from memory uses battery. If you're constantly closing and opening apps, you're repeatedly loading it and removing it from memory whereas if you just left it 'suspended', it wouldn't need to waste battery reloading into memory. I never close any apps unless it's malfunctioning.
^^^
This.

iOS and android are quite good at ram management (pure android atleast). Task manager apps and force closing has long been know to cause more harm than good.

The exception is when an app is in an unstable. state force closing is needed in those situations.
 
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