Question

Between any two given rational numbers, there are infinite rational numbers.

• A. True
• B. False

Answer 1

The correct option is A

True

There are infinite rational numbers between any two rational numbers. Let's consider an example to understand this better.

Rational numbers between $\frac{-1}{10}$ and $\frac{3}{10}$:

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

But $\frac{-1}{10}$ can be written as $\frac{-10000}{100000}$ and $\frac{3}{10}$ = $\frac{30000}{100000}$

So, rational numbers 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.