What is the exact value of pi?

Pi is the ratio of the circumference of a circle to its diameter. It cannot be written exactly as a decimal because it is a transcendental number; it's irrational. We know exactly how much it is mathematically, just like we know exactly how much the square root of 2 is, but we can't write either pi or the square root of two as a fraction of integers or as a decimal number with a repeating portion (which is the same thing). To write its decimal equivalent, we'd have digits go on to infinity without repetition.

The number of digits to which pi has been computed to thousands of thousands of millions of decimal places. The links below can show you pi to millions of digits.

Here, meanwhile, is pi to 100 significant figures:

3.14159265358979323846264338327950288419716939937510582097
4944592307816406286208998628034825342117067...

The improper fraction 355/113 is an approximation of pi accurate to six decimal places. 22/7 is an estimate.

Pi can be written down exactly as an infinite series. The equation cannot be written here due to the limited use of symbols and formats, but it can be found by using the link below to the Wikipedia post on the gamma function.

One of the interesting properties of this function is that when evaluated at 1/2, the answer is the square root of pi. By taking the square of the gamma function evaluated at 1/2, you do have the exact value of pi. The downside, however, is that saying the function isn't easy to work with for most values is an understatement.

First answer by ID3451680007. Last edit by Pure.mathmo. Contributor trust: 70 [recommend contributor]. Question popularity: 72 [recommend question]