What is the accuracy of the parallax method?
For far-distant space bodies, it is utmost three significant digits (3-sd) in AU/parsec/light year units, against the device-precision 0, 001'', for angular measurements < 1''.
The precision increases when distance decreases.
Yet, for far-distant space bodies, the parallax angle might be < i".
The precision in angular measurement is 0.001 second..
Consider the distance formula, d = 1/(angular spacing in radian) AU
This would give utmost 3-sd accuracy only in AU units. Indeed, this applies to conversion for larger units, light year and parsec..
For example, if the parallax angle is 0.127'', d = 1.62 X 10^3 AU, rounded to 3-sd approximation. The truncated and discarded digits cannot be claimed to be error-free.
If the angular precision is improved in the instrument to smaller 0.0001'', we have 4-sd approximations. ,