Question

When is it possible to find a rational number between two given rational numbers?(1 point) Responses It is possible only when the difference between the two given numbers is at least 0.00001. It is possible only when the difference between the two given numbers is at least 0.00001. 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.

Answer 1

The correct response is: It is always possible to find a rational number between any two rational numbers.

This is because rational numbers are dense in the real numbers, meaning that between any two rational numbers, no matter how close they are to each other, there exists another rational number. For example, if you have two rational numbers \( a \) and \( b \) where \( a < b \), you can always find a rational number such as \( \frac{a + b}{2} \) (the average of \( a \) and \( b \)) that lies between them.