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They can. And if you include repeating 0s and repeating 9s, then all rational numbers can be written with infinitely long repeating digits.
You can make: 1 combination containing 0 digits, 7 combinations containing 1 digits, 21 combinations containing 2 digits, 35 combinations containing 3 digits, 35 combinations containing 4 digits, 21 combinations containing 5 digits, 7 combinations containing 6 digits, and 1 combinations containing 7 digits. That makes 2^7 = 128 in all.
either irrational numbers, integers, integers, rational numbers, or whole numbers
A repeating sequence of numbers ! The digits 123456789 are simply repeated over and over.
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All decimals that terminate, or end with a repeating set of digits are rational numbers. eg 1.234, 1.222..., 1.232323..., 1.23444..., 1.2343434... are all rational numbers.
A repeating fraction is a decimal representation of a number in which a string of numbers repeats itself endlessly. The repeating string may start after a finite number of non-repeating digits. For example, 29/132 = 0.21969696... repeating. The repeated sequence is [96] which starts after two digits.
The fraction 1/7 has the decimal value 0.142857142857142857..... The six digits 142857 keep repeating.
3.14 has a finite number of digits. All numbers with a finite number of digits are rational. Pi has an infinite number of digits, AND the digits don't repeat in a regular pattern. (Numbers with repeating decimals are rational as well.)
4111 is an integer and so there is no sensible way to convert it into a repeating decimal.
Repeating Decimal
5.68 is rational. All decimal numbers that terminate, or end in one or more repeating digits are rational numbers.