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Real numbers are all numbers which do not contain "i", when "i" represents the square root of -1. All numbers which do contain "i" are "imaginary numbers" and are not real numbers.

This means that all numbers you'd ordinarily use are real numbers - all the counting numbers (integers) and all decimals are real numbers. So in answer to your question, all the real numbers that are not whole numbers are all the decimal numbers - including irrational decimals such as pi.

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Q: What are the real numbers that is not a whole number?
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No, most real numbers are not whole numbers.


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