# Question : Between any two rational numbers

- there is no rational number
- there is exactly one rational number
- there are infinitely many rational numbers
- there are only rational numbers and no irrational numbers

**Solution :**

The correct option is

**3.**there are infinitely many rational numbers

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

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

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.