Ubuntu16.04 Want to change the DNS IP Address to Google Public 8.8.8.8
I have tried Edit. NETWORK Connections >> Wireless >> Wireless Network. Then EDIT. Select IPv4 I have Automatic(DHCP). The only othe choice is
Manual. I enter the DNS Server 8.8.8.8 and then apply. Back in Details
I have my old DNS IP Addresses followed by Google Public.
I just went back through the procedure as I tried to document this. Now
I have just the google Public 8.8.8.8 in DNS. Not sure what happened
perhaps the reboot but I guess the supposed problem is solved. Unless you have some wisdom to pass on i will close the query.
Thanks ken i do need all the wisdom i can get

Thanks for the update. I am using Ubuntu16.04 with Gnome. Also, using DHCP. I used the Edit procedure from above
and now in Details I have only 8.8.8.8 & 8.8.4.4 which is what I want. This AM I did the following:
GREP -ril "8.8.8.8" /etc
I had several hits but the interesting one is etc/NetworkManager/System-Connections/2594 my wireless ID
I cannot OPEN 2594 but I suspect that is where DHCP is keeping the Network Information.
as I said I have google public as my DNS which is what I want but am now curious how it all works. so if you have
no time to waste I will close the Inquiry. Thanks ken

Some questions:

What distro/version are you using? This may not be relevant, but different distros may store ip information in slightly different locations.

Are you using DHCP or a static ip address? If you are using DHCP, you likely need to make this change in your router, as DHCP commonly gets DNS and Gateway from the router along with the ip address.