If the physical number is worn off or unreachable, you can find it in the Fitbit app by going to Account > Your Device, or via your desktop dashboard settings.

Having this 12-digit/letter sequence saved ensures you can easily replace it via warranty or prove it is yours if it is returned. File a warranty claim for your Fitbit device - Google Help

The serial number is typically printed in very small text on the rear of the device.

Finding the serial number (SN) on a Fitbit Zip is crucial for support, as it is often worn off or tiny on the back of the device.