iPhone 5 Battery draining when it's a sleep?

[gamecube117]

So last night I charged my phone. In 3 hours, it was 100% (from 0%).

I pulled the charger off, and this morning when I checked it's at 88%. It's not being used, it's shut off (not turned off), and it trained 12%. Can someone explain to me why?

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I'm wondering if it's because I had apps running (which I didn't know I had running). Someone told me to double click the button, and exit whatever I see there... and basically all my apps were there. Could this be the reason?

 

[aepple]

the battery shouldn't drain when the phone is turned off, take it to Apple and let them check it out, they may replace it with a new one. An Apple tech at the Genus bar told me they have iPhone 5's in stock for replacements only.