back up my phone numbers to my computer
How do I back up my phone numbers from my Moto G 1st gen phone to my computer, in case my phone battery goes dead?
If by backup phone numbers you mean contacts, unless you’ve taken proactive steps to stop it, contacts are already being synced to your Google (Gmail) account. You can check by pointing your computer’s web browser to contacts.google.com.
I’ve also used this app to make a redundant backup: MCBackup - My Contacts Backup - Android Apps on Google Play.
Finally, your phone won’t lose your contacts or other content merely because the battery dies. Smartphone memory is persistent. Once recharged, it will all be there.