Final answer:
To calculate the circumference of a circle the size of the known universe with an accuracy of within the radius of one proton, you would need to use approximately 16 decimal places of pi.
Step-by-step explanation:
To calculate the circumference of a circle the size of the known universe with an accuracy of within the radius of one proton, you would need to use approximately 16 decimal places of pi.
The value of pi is approximately 3.141592653589793238, but for this calculation, you would need to use more decimal places to achieve the required accuracy.
Using 16 decimal places of pi would ensure that the calculated circumference is accurate to within the radius of one proton.