hey dude you should clarify what you're saying. By "close" you seem to mean just turning off the screen by hitting that top button (often called the Sleep/Wake button). When you say it drains several percentages what is the timespan? Your phone is still "on" when the screen is black... if you let that phone sit for hours it will eventually die since it's still on. As mentioned before, in order to completely turn the phone OFF, you'd need to hold down that top button until a red arrow "slide to power off" icon appears.
If it's draining abnormally quick, you might have a weird app that is running in the background even when the screen is off. I've heard of some apps, for example, that utilize the location services, but is constantly sending updates to and from your phone. My buddy had this (not very popular) app that would let his friends know where he was at all time. In other words, they could open the app and see his location in realtime. The problem was, the way that works it was constantly using the "location services" (GPS feature) and sending updates to a server... he found that it was draining his battery really quickly.
The other thing people don't realize about the iphone is that it's technically a multitasking device. Applications stay open once you've opened them. Simply clicking the "home" button does NOT close the apps completely from memory. In order to close them, you need to double tap the "home" button... the icons of opened apps will appear on the bottom of the screen... then tap and hold on one of those apps for a couple seconds and a little red mark will appear on the left corner of the icons that will let you close those opened apps. It's really easy, but somewhat confusing to explain over text... so watch this video:
http://www.youtube.com/watch?v=xeOdVlqO-9kThat might help. You could also try completely rebooting the device which you can do by holding the "home" button and the top "close" (often called the Sleep/Wake) button at the same time. Keep holding it while the phone automatically turns off... then it will turn on again when the apple logo appears.
If none of that is helping you may have a faulty battery or something, but I doubt it. More likely you're just not very technically savvy and you're confused. Make sure you have installed the latest iphone OS by plugging it into your computer (with itunes installed) and letting itunes update it with the newest software.