Between two rational numbers(A) there is no rational number(B) there is exactly one rational number(C) there are infinitely many rational numbers(D) there are only rational numbers and no irrational numbers

The correct answer is (C) there are infinitely many rational numbers.

Here's why:

Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers (with the denominator not being zero).

Let's take two rational numbers, for example, 1/2 and 3/4.

Step 1: To find a rational number between these two, you can simply add them together and then divide by 2.

(1/2 + 3/4) / 2 = 5/8

So, 5/8 is a rational number that lies between 1/2 and 3/4.

Step 2: You can repeat this process with 1/2 and 5/8 to find another rational number that lies between them.

(1/2 + 5/8) / 2 = 9/16

So, 9/16 is another rational number that lies between 1/2 and 5/8.

You can keep repeating this process to find more and more rational numbers that lie between the original two. Therefore, there are infinitely many rational numbers between any two rational numbers.