I heard this on the radio today that while the value of pi has been computed to more than a trillion digits, elementary applications, such as calculating the circumference of a circle, will rarely require more than a dozen decimal places. For example, a value truncated to 39 decimal places is sufficient to compute the circumference of any circle that fits in the observable universe to a precision comparable to the size of a hydrogen atom.
I also remember reading that when the first Appollo moon shots were made, that they just used 3.14 in all their calculations.