Charging Problems and Battery Life

[officialcitrus]

So, I just got a Bionic for Christmas, I like it so far, but I've had this problem twice now.

Today, I tried installing some app updates. For some reason or another they weren't downloading, and I saw that my battery life was dropping fast, so I turned off the phone to cancel the updates. When it came back on there was only 20% battery left, so I went and plugged it in. I had to leave before it was fully charged, so when I unplugged it, it said there was 70% battery. Within an hour and a half, the phone was dead, completely. I was surprised, because it supposedly had 70% battery, but not too worried. Battery indicators have never been particularly accurate. But when I plugged it in again, it wouldn't charge at all. I pulled the battery out and plugged it in with no battery to get it to come on, then I put the battery back in and now it's charging. The first time this happened was the day I got it (everything was the same except for the part about the updates, the battery just ran down cause it wasn't fully charged when he sold it to me).

Also, just now I turned the phone on after it had charged up a bit, and it read 70% battery. I locked it, and immediately unlocked it again, and it said 100%. I really don't understand.

Is there a problem with the phone? Or maybe the battery? Or is this normal?

Thanks!