When is it possible to find a rational number between two given rational numbers?(1 point)ResponsesIt 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 two given numbers are positive.It is possible only when the two given numbers are positive.It is possible only when the difference between the two given numbers is at least 0.00001.
1 answer
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 number line, meaning that between any two rational numbers, 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 like \( \frac{a+b}{2} \), which is the average of the two.
