I thought I heard that NASA did a lot of their computations in base 12 math, in which pi is a rational number. And I heard that decades ago.
In everyday calculations not requiring much precision, 3.14159 is sufficient for getting answers that are ‘close enough’.
But when you’re dealing with astronomical numbers measured in parsecs or light years, then those extra added digits become quite relevant to your equations.....................
Pi is not a rational number in any integral base. If it was rational in a particular base, then it would be represented as the quotient of two integers in that base. Converting both integers to base 10, we would have a representation of pi as a rational number (in base 10). But pi is not rational in base 10.
An irrational number is irrational, no matter what base is used.
NASA would be full of idiots if they thought Pi was rational in any base. Or perhaps the source you heard it from is the idiot.