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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Yes. Every number is a real number. Rational numbers, irrational numbers, Whole numbers, Natural numbers, integers are all real numbers.
Yes. The set of whole numbers (more usually called Integers) is a strict subset of the set of Real Numbers.
No. There are several real numbers that are not rational (e.g. pi). However, every rational number is also a real number. In general, whole numbers/natural numbers is a subset of the integers (i.e. every whole number is an integer), the integers is a subset of the rationals, the rationals are a subset of the real numbers. I think the real numbers are a subset of the complex numbers, but I'm not 100% positive on that.
No, a real number could also be a rational number, an integer, a whole number, or a natural number. Irrational numbers fall into the same category of real numbers, but every real number is not an irrational number.
56 is a rational whole natural number. Or to put it another way: 56 is a Natural number, but as all natural numbers are also whole numbers 56 is also a whole number, but as all whole numbers are also rational numbers 56 is also a rational number. Natural numbers are a [proper] subset of whole numbers; Whole numbers are a [proper] subset of rational numbers. The set of rational numbers along with the set of irrational numbers make up the set of real numbers