Question

How many rational numbers are there between two rational numbers?

• A. $1$
• B. $0$
• C. Unlimited
• D. $100$

Answer 1

The correct option is C

Unlimited

Explanation for the correct option:

Determine number of rational numbers between two rational numbers:

1. A rational number is of the form $\frac{p}{q}$, $p$ and $q$ are integers where $p$ is not equal to 0.
2. A rational number can also be denoted in decimal form.
3. It can be a terminating decimal or recurring decimal.

For example, consider two rational numbers $\frac{21}{10}$ and $\frac{31}{10}$.

So, the rational numbers between $\frac{21}{10}$ and $\frac{31}{10}$ are $\frac{211}{100},\frac{2111}{1000},\frac{21111}{10000},\frac{22}{10}$ and so on.

Thus, there are an unlimited number of rational numbers between two rational numbers.

Hence, option C is correct.