Question

Between two given rational numbers, there are rational numbers.

• A. only one
• B. exactly ten
• C. infinitely many
• D. exactly two

Answer 1

The correct option is C infinitely many

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

For example, rational numbers between $\frac{-1}{10}$ and $\frac{3}{10}$ are

$\frac{0}{10}$, $\frac{1}{10}$, $\frac{2}{10}$

But $\frac{-1}{10}$ can be written as $\frac{-10000}{100000}$ and $\frac{3}{10}$ = $\frac{30000}{100000}$
So, rational number between $\frac{-1}{10}$ and $\frac{3}{10}$ are $\frac{-9999}{100000}$, $\frac{-9998}{100000}$ ,…..$\frac{29998}{100000}$, $\frac{299999}{100000}$
Thus, we can find infinite rational numbers between any two rational numbers.