I have 1/10 of a Bitcoin that I bought in 2014 stored on my Bitcoin app on my Android phone, which died. The repair service may be able to transfer the phone's data onto my new phone. If this is not possible, then is my Bitcoin lost forever?

You would need access to the private key that only exists on that phone. That same phone has to be rebooted. Did you set up a backup when you downloaded the wallet?

Thanks Kelvin. I did back it up when I set up my wallet. I can't reboot my phone because it doesn't turn on. I hope that the repair place can do this when they transfer the data. But will the key transfer? Is the key part of my Bitcoin app on my broken phone?