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Is the number 0.112123123412345. a rational or irrational number?
It's rational. It can be written as the quotient of two numbers whose HCF is one.
Is pi divided by e rational?
A rational number is able to be represented as a ratio of polynomials. pi/e is a ratio of irrational numbers, neither of which can be represented as a ratio of polynomials, and so I would conclude that pi/e is not rational. But it's a good question, because what if two irrational numbers could cancel out their irrationality, like two negative numbers! A quotient of two irrational numbers can be a rational number. Trivial example 2pi/pi = 2.
Are real numbers rational and irrational?
The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.
Numbers existing between two rational numbers?
There are more irrational numbers between any two rational numbers than there are rational numbers in total.
How many rational numbers can be inserted between two irrational numbers?
Infinitely many! There are an infinite number of rational numbers between any two irrational numbers (they will more than likely have very large numerators and denominators), and there are an infinite number of irrational numbers between any two rational numbers.
