When is it possible to find a rational number between two given rational numbers?
1) It is possible only when the difference between the two given numbers is at least 0.00001.
2) It is possible only when the two given numbers are positive.
3) It is always possible to find a rational number between any two rational numbers.
4) It is possible only when the two given numbers are integers.
The correct statement is option 3) It is always possible to find a rational number between any two rational numbers.
This statement is true because between any two rational numbers, there is an infinite number of rational numbers. This can be proven by taking the average of the two given numbers, which will always result in a rational number. Therefore, it is always possible to find a rational number between any two rational numbers.
The correct answer is option 3) It is always possible to find a rational number between any two rational numbers.
Explanation:
Rational numbers are numbers that can be expressed as a quotient (or fraction) of two integers, where the denominator is not zero.
Given two rational numbers, we can always find a rational number between them by taking the average of the two numbers. For example, if we have rational numbers a/b and c/d, where a/b < c/d, the rational number (a/b + c/d)/2 is between them.
Therefore, it is always possible to find a rational number between any two given rational numbers.