A repeating decimal is a rational number. Its value is
(the repeating set of digits)/(as many 9s as there are digits above).
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Repeating decimals are rational numbers if there is a pattern, like 0.22222222. If it is not a pattern, like 0.568964329, it is an irrational number.
Irrational numbers are non-repeating, non-terminating decimals. If your number repeats, it's rational. If it doesn't, it's irrational.
Non-repeating, non-terminating decimals.
Actually, a repeating decimal is not necessarily an irrational number. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. While some repeating decimals can be irrational, such as 0.1010010001..., others can be rational, like 0.3333... which is equal to 1/3. Irrational numbers are numbers that cannot be expressed as a simple fraction, and they have non-repeating, non-terminating decimal representations.
This number is rational as 0.151155111555 = 151155111555 / 1000000000000 = 151291 / 1000899 if 0.151155111555 is the beginning of the number 0.151155111555111155551111155555.... then it's irrational as the decimals are not repeating and the sequence is infinite