If you think you’ve closed an app by holding the Home button and swiping at it, think again. Many apps run separate processes that can zap your battery. To make sure that your GS4 is only running what is absolutely necessary, be sure to open the Task Manager by holding the Home button and then tapping the pie chart icon. From here, you can quickly and safely kill a number of applications with the “End all” button.
If you want extra peace of mind, tap the Clear Memory button under the RAM tab to safely kill all processes that can be closed with a single tap. Not enough for you? Go to the Application Manager under the More tab within Settings. From here, you can individually close the processes that the above methods didn't touch. But beware: Do not kill a process unless you know exactly what it does; otherwise, you could end up seriously impacting your device’s functionality.