They don't use batteries though. They get all the energy they need through the signal being sent to them. The signal is so weak that no damage will happen to the surrounding tissue. According to documentaries I've seen and read about these chips, we're constantly bombarded by radio signals much stronger than those used to scan these chips. Animals have been chipped for many years with no effects to the animal.
Mobile phones emits very strong radio signals, especially when sending or receiving a phone call, yet most of us carry one around strapped to our body.
I've read some articles where animals have developed tumours and sores from wearing microchips.