When is it possible to find a rational number between two given rational numbers?(1 point)

Question

Responses

It is possible only when the two given numbers are positive.
It is possible only when the two given numbers are positive.

It is always possible to find a rational number between any two rational numbers.
It is always possible to find a rational number between any two rational numbers.

It is possible only when the two given numbers are integers.
It is possible only when the two given numbers are integers.

It is possible only when the difference between the two given numbers is at least 0.00001.

Answer 1

The correct response is:

It is always possible to find a rational number between any two rational numbers.

This is due to the density of rational numbers on the number line; no matter how close two rational numbers are, you can always find another rational number between them. For example, for any two rational numbers $a$ and $b$ (where $a<b$), the number $\frac{a+b}{2}$ is a rational number that lies between $a$ and $b$.