Tony's 5.74 decimal degrees [or 5° 44' 24"] produces a geometric .0001 movement of the compound; actual movement is theoretical depending on accuracy of dial and thread pitch built into lathe. As he states, an indicator resolve better than the screw & dial alone.
The problem's root? Conversion of manual torque overcoming stiction to rotary motion [screw & dial] into the linear of any slide motion. Add counteracting manufacturing tolerances of equipment itself...
Unless your lathe has [a]very large diameter dials, [b]a vernier, [c]gibs and [d]backlash well set, and [e]screw/ nut combination are very smooth operating, such fine increments are difficult to attain. A 1/10th by lathe cross slide is virtually impossible; while a good old jig bore can do that with no fuss; utilizing the details above. Can you imagine threading Class 3 or 4 fits without a cross slide? Yikes!
DRO's are fine, but size changes in turning and boring are dependent on good/ ideal mechanical conditions to support the digital readings. It matters when only 1 piece of stock is available for a complex part.
Another convenient angle is 30° 00' 00"; generating half-thousandths easily by a sine of 0.5000. Very handy on lathes with direct .001 graduations that affect diameters by .002.
DRO or not, personally I set compounds 0°, 5° 44' 24", 29° 30' 00'', 30° 00' 00'' and/or 90° 00' 00" according to job being run, considering design features with tolerances. Occasionally this requires altering settings to complete a part.
I'd say 29° 30' is my normal setting. Ready to thread, close enough for .0005 size control, and imparts smooth movement for 45° ID/OD chamfer form tools. On larger lathes, mass helps with cut-off tools, 29° 30' is OK. Small machines I set 0° [straight in].