Final answer:
Span between a rational and an irrational number means to find numbers that lie between them on the number line. Rational numbers can be expressed as fractions, while irrational numbers have non-terminating, non-repeating decimal forms. There are infinitely many rational and irrational numbers between any two distinct real numbers.
Step-by-step explanation:
To clarify, it seems the question asks how to span between a rational number and an irrational number. In mathematics, a rational number is any number that can be expressed as a fraction a/b, where a is an integer and b is a non-zero integer. On the other hand, an irrational number cannot be expressed as a simple fraction; it's decimal form is non-terminating and non-repeating.
An example of a rational number is 3/4, which equals 0.75 when written as a decimal. An example of an irrational number is the square root of 2, which is approximately equal to 1.41421 and goes on infinitely without repeating. To span between a rational and an irrational number means to identify numbers that lie between them on the number line. For example, between the rational number 1.4 and the irrational number sqrt(2), you could find both rational numbers-like 1.41, 1.42 - and other irrational numbers-like the square root of 1.99.
It's important to note that between any two distinct real numbers, there are infinitely many rational and irrational numbers. To demonstrate this, you could use a method like finding midpoints or by adding a small value to the lower number until you approach the higher number without ever reaching it.