Question

Between any 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

Answer 1

Answer: (C)

there are infinitely many rational numbers

Recall that to find a rational number between $r$ and $s,$ you can add

$r$ and $s$ and divide the sum by $2,$ that is $\frac{r+s}{2}$ lies between r and s.

For example, $\frac{5}{2}$ is a number between $2$ and

$3.$ We can proceed in this manner to find many more rational numbers between $2$ and $3.$

Hence, we can conclude that there are infinitely many rational numbers between any two given rational numbers.