Yes. There are infinitely many rational numbers between any two real numbers.
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Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All rational numbers are real.
No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.
No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.
Yes, a rational number is a real number. A rational number is a number that can be written as the quotient of two integers, a/b, where b does not equal 0. Integers are real numbers. The quotient of two real numbers is always a real number. The terms "rational" and "irrational" apply to the real numbers. There is no corresponding concept for any other types of numbers.
247 is both a rational and real number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers, and 247 can be written as 247/1. Real numbers include all rational numbers, as well as irrational numbers, and since 247 is a rational number, it falls under the category of real numbers.