Gnome 3.16 HiDPI scaling only accepts integers

I checked with my Fedora 21 install where I have Gnome 3.14.2 and it doesn't seem to be possible to set your desired value:

[btegge@za21 ~]$ gsettings set org.gnome.desktop.interface scaling-factor 1.2
invalid character in number:
  1.2
   ^
[btegge@za21 ~]$ gsettings set org.gnome.desktop.interface scaling-factor 1,2
expected end of input:
  1,2
   ^

My assumptions:

• There is a another setting to achieve what you want. The only thing that comes to my mind is font rendering related, though that is not exactly what you are looking for.
• It's a mistake that the key only accepts integers as datatype and you should file a bug.

I am not sure if this got resolved or not, but there are two scaling options in Gnome to achieve this. The "window scaling" attribute that you are doing either accepts 1 or 2 (or 0, but this is "undefined" I think). If you want, you can do text scaling, which accepts floating numbers.

In Gnome Tweak Tool, this is available under the font section. Alternatively, you can access both in the dconf-editor under org.gnome.desktop.interface I have noticed this option tends to work better, as Gnome Tweak Tool can sometimes not update setting correctly, causing weird scaling issues.

Fractional scaling is not officially supported on versions lower than 3.32 and not supported at all inside GNOME in versions lower than 3.28.

You can neverthless obtain the same effect on 3.16 with xrandr.

You can do it if you switch to the Wayland display server: https://www.omgubuntu.co.uk/2017/09/enable-fractional-scaling-gnome-linux

Otherwise, your only option would seem to be to upgrade to a version of the distro with a newer version of GNOME. This functionality is available in Ubuntu 19.04: https://www.omgubuntu.co.uk/2019/06/enable-fractional-scaling-ubuntu-19-04