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.
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Irrational numbers are non-repeating, non-terminating decimals. If your number repeats, it's rational. If it doesn't, it's irrational.
1.777...(repeating) is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
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.
Non-repeating, non-terminating decimals.
If you convert them into decimal form you can say there are terminating decimals, there are the integers, and there are repeating decimals. EX: 2.4 is a terminating decimal. 2.44444444... is a repeating decimal. 2 is an integer. all are rational numbers.