John Gruber writing about force quitting apps to save battery:
The iOS system is designed so that none of the above justifications for force quitting are true. Apps in the background are effectively “frozen”, severely limiting what they can do in the background and freeing up the RAM they were using. iOS is really, really good at this. It is so good at this that unfreezing a frozen app takes up way less CPU (and energy) than relaunching an app that had been force quit. Not only does force quitting your apps not help, it actually hurts. Your battery life will be worse and it will take much longer to switch apps if you force quit apps in the background.