The decimal digits of Pi never end; they continue infinitely. The digits also will never repeat. These are characteristics of Irrational Numbers. Rational numbers have decimal fractions that either come to an exact end, or they fall at some point into an infinitely repeating pattern. 1/5 equals .25 exactly, and 1/3 has a repeating decimal fraction of .3333_.
So far pi has been calculated out to at least 2.7 trillion decimal places, and since irrational numbers go on for infinitely many decimal places, we are nowhere near the end (and never will be, however hard we try). To keep things in perspective, by the time you reach 6 or 8 decimal places, you have pi to a tolerance good enough for almost any application we could ever imagine using on a practical level. If we ever need more decimal places than 8, we can go to the above calculation where there are a few waiting in the wings.
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An irrational number, for example pi or e or the square root of 2
Pi is not rational it is irrational because it does not stop or repeat
Pi is an irrational number. That means that it never stops and will never repeat itself. The first 85 decimals without rounding are 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280...
"...although many mathematicians have tried to find it, no repeating pattern for pi has been discovered..." (http://mathforum.org/dr.math/faq/faq.pi.html).
Decimals repeat because there is no definite end. In these, you can end the repeat by rounding up... (Exp: 4.44444444444444... would be 4.45 or 4.445 or 4.4445, etc.