Question

We can find _____ rational number(s) between any two rational numbers.

• A. not more than two
• B. zero
• C. infinitely many
• D. one and only one

Answer 1

The correct option is C

infinitely many

There will be countless rational numbers between any two rational numbers.

For example, let us try finding a few rational numbers between the rational numbers $\frac{-1}{10}$ and $\frac{3}{10}$.

$\frac{0}{10}$, $\frac{1}{10}$, $\frac{2}{10}$ are the obvious rational numbers between them.

Also, $\frac{-1}{10}$ can be written as $\frac{-10000}{100000}$ and $\frac{3}{10}$ can be written as $\frac{30000}{100000}$.

So, rational number between $\frac{-1}{10}$ and $\frac{3}{10}$ are $\frac{-9999}{100000}$, $\frac{-9998}{100000}$ ,…..$\frac{29998}{100000}$, $\frac{29999}{100000}$.

Thus, we can find infinite rational numbers between any two rational numbers.