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Just tested it myself. It seems to be saved properly:
set dopplertool:freq_rate 10.012345678
dopplertool:freq_rate = 10.012345678
get dopplertool:freq_rate
dopplertool:freq_rate = 10.012345678
The GUI is limited to 3 decimal places, and I believe that is fine for most manual corrections (1 mHz/s is something that varies slowly, in the order of several minutes to a few hours fonr 1 Hz change). On the other hand, I do acknowledge that it would be desirable to have a fixed precision output (right now it computes the display precision automatically). I will definitely change that.
When I use the server to change the "Freq rate" value, it rounds to 2 decimal places.
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