maccawacca Seconds 05.3. I am sure the .3 would be vitally important to find the target.
Because of the earth's rotation, a star moves 360 degrees per 23 hours 56 minutes of time. It is not 24 hours because the earth also moves 360º every 365.25 days in its orbit around the Sun. The Right Ascension (RA) therefore moves at the same rate as you track a star across the night sky.
360º per 24 hours corresponds to a rate of 15º per hour, or 15' per minute (of time) and 15" per second (of time).
Your mount, together with ASIAIR's rounding error has a total error of 0.3 seconds of Right Ascension (time). This therefore correspond to 0.3*15 (the 15 is the rate), or 4.5 arc seconds in the sky.
To give you an idea of how large 4.5 arc seconds is, a typical plate scale (combination of the focal length of the OTA and the pixel size of the camera) is around 1 arc second per pixel. Thus, the 4.5 arc second error would correspond to 4.5 pixels (depending on your plate scale, probably in the range of 2 to 8 pixels).
One way to visualize the magnitude of the error is that your camera sensor is likely to have (low single digits of) thousands of pixels wide. You will hardly even be able to see 0.3 seconds of Right Ascension error on the ASIAIR Preview window.
Another way to visualize the size of the error is that the Moon is about 1800 arc seconds in diameter, and Jupiter at opposition is about 50 arc seconds in diameter. The 4.5 arc second error is about the size of Jupiter's Great Red Spot.
The ASIAIR always had this rounding error when reading back coordinates from the mount. It has been mentioned a couple of times on different forums, but ZWO never bothered to fix this error. You will find this to be true after a series of plate solves too. You just have to live with it. And since it is small, just ignore it.
Chen