Why does my iphone battery run down when it is switched off?

I charged my iphone 3gs just before i went to bed last night and then switched it off (the battery was at 85%) but when i woke up this morning and switched it on it was down to 20% why does it run down so fast if it wasn't even on!

You need to understand smart fone are like computers ans take a lot odd power to switch on you are more likely to save battery by leaving the phone on and switching Wi-Fi ans 3g off

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