We use the decimal system for imperial units too. Thousands of an inch, millionths of an inch, etc.

In most practical applications that I've seen fractions of imperial measurements used, it tends to be in powers of 2, i.e., 3/16 inch, 1/4 mile, etc. Decimals can certainly be used, but for most applications where you'd use something like a "millionth of an inch," it's vastly more common to use metric.

What applications are you talking about? Just for a general example of the sort of thing I'm talking about: https://youtu.be/EWqThb9Z1jk?t=137

They're resurfacing a surface plate, which has to be very flat. If you listen to the exchanges between them, everything is being done in millionths of an inch.

In my experience (electronics manufacturing), both PCBs and machined parts are usually in mils or decimal inches, although millimeters are becoming more common and many drawings show both systems.

This might be specific to where you live though, in my experience in the electronics industry, I've pretty much only seen millimeters.

Or nothing is stopping you from using things like 1.3 inches, 2.7 miles, .6 gallons. I tend to use the fractions when doing measurements in my head. But if things get too complicated and I have a calculator I switch to decimal.