Such numbers can be written in the form of a ratio of two integers. In the first case as a ratio of an integer and a power of ten, and in the second case as a ratio of an integer and one less than a power of ten. Since the denominators in both cases are non-zero integers, these are rational numbers.
Examples:
0.356 = 356/1000
0.356356356... (repeating) = 356/999
In the first case the number of zeros after 1 is the number of digits after the decimal point. In the second case, the number of 9s is one fewer than the length of the repeating string.
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Terminating and repeating decimals are rational numbers.
Yes.
Yes.
Yes. Rational numbers are numbers or decimals that repeat or terminate. Irrational numbers do not. For example π is an irrational number.
Yes, they will.