Question

Between two given rational numbers, we can find
(a) one and only one rational number.
(b) only two rational numbers.
(c) only ten rational numbers.
(d) infinitely many rational numbers.

Answer 1

We can find infinitely many rational numbers between two given rational numbers.

Suppose two rational numbers $\frac{2}{5}$ and $\frac{7}{5}$, we can find $\frac{3}{5},\frac{4}{5},\frac{5}{5},$ and $\frac{6}{5}$ rational numbers between these $\frac{2}{5}$ and $\frac{7}{5}$.

We can write equivalent rational numbers of $\frac{2}{5}$ and $\frac{7}{5}$ as

$\frac{2\times 5}{5\times 5}=\frac{10}{25}$

$\frac{7\times 5}{5\times 5}=\frac{35}{25}$

so, now rational numbers between $\frac{10}{25}$ and $\frac{35}{25}$ are $\frac{11}{25},$ $\frac{12}{25}\dots \dots$

In this way we can find infinite rational numbers between any two rational numbers.

Hence, the correct option is (d).