First you must realize that a flash drive has a very limited life
span.  Booting it several times a day will decrease that life span. 
That said, when you install an OS to a flash drive you generally

First you must realize that a flash drive has a very limited life span.  Booting it several times a day will decrease that life span.  That said, when you install an OS to a flash drive you generally have three options; a live image, a live image with persistence, or a regular install.  The live image starts with a blank slate every time you boot it.  The live image with persistence retains some changes.  Any changes you make to the system—for example, saving a file to your desktop, changing the settings in an application, or installing a program—will be stored in the overlay file.  Whenever you boot the USB drive on any computer, your files, settings, and installed programs will be there.  There are a few limitations. You can’t modify system files, like the kernel.  You can’t perform major system upgrades.  You also can’t install hardware drivers.  However, you can install most applications.  You can even update most installed applications, so you can be sure your persistent USB drive has the latest version of the web browser you prefer.  The regular install to a flash drive treats the flash drive as a hard drive which of course it is.  
See here for a definition and the advantages and disadvantages of installing with persistence.  https://www.pendrivelinux.com/what-is-persistent-linux/
There are any number of sites that explain how to install an OS to a flash drive with persistence.   https://askubuntu.com/questions/401273/how-do-you-create-a-live-persistent-ubuntu-usb-on-a-mac-that-will-boot-to-a-mac 

Rex Bouwense

On 01/09/2018 10:46 AM, Charles Breaux wrote:

ubuntu-16.04.3-desktop-amd64.isoHow to convert .iso to .img using Disk Utility on a mac.

All I did was use Disk Utility, click the .iso file>drag to disk image section of Disk Utility>click Convert>save with a .dmg. And then burned a dvd.

But, I instead of making a dual boot system, I want to burn a persistent USB. (I had bad luck one time installing ubuntu dual boot with windows. I had done this several times and was aware of how to do it, etc. Nonetheless, when I installed ubuntu it erased my windows, so I’m leary of installing a dual boot on my Mac as I don’t have an install disc for my mac os, and my HD is a small ssd)

I did this with another USB for my pc computers. I simply used and install disc to instal ubuntu onto a USB rather than the HD—and easy way to create a persistent USB. Worked great. But, When I tried installing the mac dmg version on a USB, I got this error:

“no root system is defined. Correct from partitioning menu” I assume that is something that I have to do when formatting the usb drive. But I don’t know how to do it.

Can anyone help me define a root system on the usb drive?