The rounding has a less significant impact than you’d think.
Interplanetary calculations of the highest precision will use just 15 decimals, which results in an error of about 1cm when calculating a circumference of 150 billion km.
But if you really want to measure even more accurately than that… The circumference of a circle with a diameter of 92 billion light years (as large as the known universe) can be calculated using 37 decimals of pi, and the result would be accurate within the width of a single hydrogen atom.
The rounding has a less significant impact than you’d think.
Interplanetary calculations of the highest precision will use just 15 decimals, which results in an error of about 1cm when calculating a circumference of 150 billion km.
But if you really want to measure even more accurately than that… The circumference of a circle with a diameter of 92 billion light years (as large as the known universe) can be calculated using 37 decimals of pi, and the result would be accurate within the width of a single hydrogen atom.
https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/