To calculate the circumference of the observable universe down to the Planck length, we need an extremely high precision value of π. However, it's important to note that the Planck length (approximately 1.616 × 10^−35 meters) is many orders of magnitude smaller than any measurable length in the observable universe.
Pi (π) is an irrational number, meaning it has infinite decimal places and cannot be expressed exactly as a fraction. The current record for calculating the most decimal places of π stands at over 31 trillion digits, which far exceeds the level of precision required for any practical application.
For most scientific and engineering purposes, a few decimal places of π are sufficient. Even using just 15 decimal places of π (3.141592653589793), the calculated circumference of the observable universe would be incredibly accurate. Going beyond that number of decimal places would not yield any meaningful change in the result when calculating at the scale of the observable universe down to the Planck length.
Therefore, it is unnecessary to calculate π to an extraordinarily high number of decimal places to determine the circumference of the observable universe down to the Planck length, as the Planck length is already far beyond the precision of any current or foreseeable measurement.