How many rational numbers lie between two rational numbers?

Infinitely many rational numbers exist between any two rational numbers. This is called the dense property of rational numbers.

Example: Between 1/2 and 1:

Using the mean method:

• (1/2 + 1)/2 = 3/4
• (1/2 + 3/4)/2 = 5/8
• (3/4 + 1)/2 = 7/8

So: 1/2 < 5/8 < 3/4 < 7/8 < 1

This process can continue forever, finding more numbers each time.

General method: If a and b are two rational numbers, then c = (a + b)/2 lies between them, and a < c < b.