Pi is the name for the Greek letter 
, which corresponds to the English letter p.
is also the symbol used in mathematics for the ratio between the diameter of a circle and its circumference, and which appears in many other places.
is an irrational number; this means that it cannot be expressed as a fraction, and (therefore) cannot be expressed exactly as a decimal no matter how many decimal places it is carried out to.
The value of is approximately 3.14159. This value is precise enough for almost all ordinary purposes; it can, for example, be used to calculate the circumference of the Earth with an error of only 350 feet.
For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used.
The number of digits to which can be calculated is an ongoing endeavour. In 1873 Abraham Shanks spent twenty years calculating to 707 places, but unfortunately made a mistake in his calculation and only 527 of them were correct. When electronic computers were developed, was soon calculated to tens of thousands, millions, and billions of places. As of 2002, the record is held by Yasumasa Kanada of Tokyo University at 1,241,100,000,000 digits.
Knowledge of the ratio of the diameter of a circle to its circumference was not limited to the Greeks. In the Bible, 1 Kings 7:23 contains the passage "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about." The Papyrys of Ahmes, dated c. 1650 B.C. shows that ancient Egyptians had a value of 3 1/6 = 3.166666667. Babylonians also had a similar ratio, at a value of 3 1/8 or 3.125.[1]
Trivia
Numerous mnemoics for remembering have been divised, including counting the letters in the phrase "Now I want a drink—alcoholic, of course," which gives to seven places (more than enough for most ordinary purposes) and Michael Keith's poem entitled Near a Raven which simultaneously parodies Edgar Allen Poe's poem The Raven, while encoding to 740 places.
Printing out at 1,241,100,000,000 digits on paper at 5000 digits per sheet would require 248,220,000 pages or 496,440 reams of paper. [2]