It won't. Once your phone goes to sleep it's not really doing much of anything except listening for incoming signals I don't think, just phone calls, push notifications, and texts.
If it drained that fast, it was due to having either push on, bluetooth on, or having a very weak signal from 3G or EDGE and your phone constantly having to search for a signal. Even if you were surfing, the battery should last 5 hours (so, 20% and hour maybe). Besides, once you close Safari, it's no longer surfing. There is a small amount of memory being used, but that won't drain the battery much.
Hi battery was down to 40%. Started browsing, made some calls, and texting. Stayed on 40% without going down. Figured I would re boot iPhone by shutting it off and then on. The battery went up from 40% to 52%.
Yes, that's normal. The exp. resedue in the battery lessens once the battery is deactivated. Once it is restarted, the battery is "clean" and will have a small precentage of pick-up.
Not only that, the battery meters in most small devices are inaccurate.