An irrational number, for example pi or e or the square root of 2
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Irrational.
Decimals can either terminate OR repeat. One decimal does not do both. Example-- 3.059 is a terminating decimal, meaning it stops. Example-- 3.059059... is a repeating decimal, meaning it repeats. You would write that as 3.059 with a line over the 0,5, and 9 because they repeat themselves.
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.
A terminating decimal
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.
The name for a decimal of this kind is "recurring".
Recurring
A number can end or repeat but it cannot end andrepeat (other than repeat 000... or 999... ).A number that can be written as a terminating or repeating decimal is a rational number.
Irrational.
It is a decimal that does not end, nor do the numberals repeat themselves in any recognizable sequence. An example is Pi.
A repeating decimal is a decimal that contains a series of numbers that repeat indefinitely. Examples include: 3.44444... 4.565656... 2.356356356... An ellipsis (...) at the end of the decimal signals that it repeats indefinitely.
Any number that can be written as a fraction:15.2=152/10 etc. Any number without a decimal or fraction: 15. Any numbers with decimal numbers that end (4, 2.5) or repeat (1/3, 55/9).
It is a repeating decimal.
The decimal form of nineteen over six is: 3.1666666666666666666666666666666666666666667 This is an approximation, since the sixes repeat forever, the 7 at the end is merely a rounding up .
No. Pi is a transcendental number which is a kind of irrational number. It has an infinite decimal representation which does not end nor does it go into a recurring cycle. That does not mean that there are no repeated digits, it simply means that digits may repeat themselves for a little while but then continue in what appears to be a random pattern. Not only does it not have an infinite decimal representation, but infinite binary, ternary, etc representations.
It is a repeating decimal.
Terminating Decimal