Don't tell your calculator about this surprising result - it'll get depressed

How many digits of pi do we really need? Eh, not that many, says NASA. - Vox

Marc Rayman, the director and chief engineer for NASA's Dawn mission, recently made this clear  in response to a question on Facebook. NASA, he explained, certainly doesn't need trillions of digits for itscalculations. In fact, they get by with using just fifteen — 3.141592653589793. It's not perfect, but it's close enough:

The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let's say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles.

We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by
1.5 inches.

Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps  less than the length of your little finger.

Going further, if you used 40 digits of pi, Rayman says, you could calculate the circumference of the entire visible universe — an area with the radius of about 46 billion light years — "to an
accuracy equal to the diameter of a hydrogen atom." That'll do!