Recently on Marilyn's discussion boards...
From sysprog:Saying that the "ratio" of the circumference of a circle to its diameter (circumference/diameter) is an ir"ratio"nal number (i.e. a number that cannot be expressed numerically as a ratio) raises the concern that the statement may on superficial parsing appear to some to be inclusive of contradiction, or that it incites in some the objection that the limit of an infinite series is by definition non-findable by finite methods, in that the series is unending, and along with that may be embraced the preposterous notion that what is not finitely findable must "ipso facto" not exist; however, the circumference/diameter ratio is indispensable for any sensible definition of "circle", and such a definition is very useful in application to the real world.
In practical real-world applications of pi, we can rely on a rational number, expressible as 3 plus a finite decimal expansion, of some arbitrarily finely measurable precision, to suffice for use-worthy representation of anything we can observe, model, or make.
In the real word everything circular is composed of a finite number (usually in the process of varying near the boundaries) of elementary particles, each of which comprises, at any arbitrary moment in time, some finite, not necessarily measurable, number and magnitude of forces and interactions thereof.
When buying tires, we want the ones that are made for the wheel diameter specified by the vehicle manufacturer, and we want the odometer to tell us how far the vehicle has rolled along -- something that may be expressed as as set of functions that reduce to a multiple of the wheel circumference. If you read your odometer, and divide its value by the exterior diameter of your tires, you'll get a number that is approximately pi times the number of times your wheels have rotated. If you use pi=3.1416, you'll be well within the precision of your odometer.
There is an old story -- I don't know whether it's true -- that a state (Indiana?) legislator once got annoyed with all the fuss about pi being an irrational number, so he introduced a bill defining pi to be equal to 3. Another legislator protested that wheels can't be made using pi=3. After some debate, the story goes, they settled on pi=22/7 -- close enough for government work.