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Answer:
Rational.
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It is:
Rational. It's real value can be expressed as the ratio of 2 integers, therefore, it's rational.
It's not:
Natural. It's not a natural number since it can't be used to count things or to order things.
Integer and whole (it's the same). It's not an integer or whole because it can't be written without a fractional component. In this case the fracional component is the period.
Irrational. It's real value can be expressed as the ratio of 2 integers, therefore, it's rational.