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In between two rational number there is/are

Question: In between two rational numbers there is/are :

  1. Only irrational number
  2. Exactly one rational number
  3. Infinitely many rational numbers
  4. Many irrational numbers
Solution :
The correct option is 1.  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.

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