They can. And if you include repeating 0s and repeating 9s, then all rational numbers can be written with infinitely long repeating digits.
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They are rational numbers.
Rational numbers can be written as a fraction with a non-zero denominator,as a terminating,a decimal,or a repeating decimal.
Yes.
A repeating decimal is any rational number whose decimal representation does not terminate after a given number of digits. As only a very small quantity of the rational numbers terminate in their decimal representation, practically any rational number picked at random will be a repeating decimal.
All real numbers have a decimal representation. Rational numbers have decimal representations that terminate or repeat infinitely. Irrational numbers have decimal representations that are non-terminating and non-repeating.