Pi.
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2, 3.67, -4.585858.. (repeating) are some examples.
It is a rational fraction.
No. Rational numbers are either terminating decimals or non-terminating BUT recurrent decimals.
All integers are rational numbers. As a result, there are no such numbers. There is, therefore, no name for these non-existent numbers.
If they are non-terminating and there is a repeating pattern, then they are rational. If they are non-terminating and there is no repeating pattern, as in pi, they are irrational.