📘 Question
Is zero a rational number? Can you write it in the form \( \frac{p}{q} \), where \(p\) and \(q\) are integers and \(q \ne 0\)?
✏️ Solution
Step 1: Definition
A rational number is any number that can be written as:
\[
\frac{p}{q}, \quad \text{where } p, q \in \mathbb{Z}, \; q \ne 0
\]
—
Step 2: Express 0 in this form
\[
0 = \frac{0}{1}
\]
Here:
- \(p = 0\)
- \(q = 1 \ne 0\)
Step 3: Conclusion
Thus, 0 satisfies the definition of a rational number.
—✅ Final Answer
Yes, 0 is a rational number because it can be written as \( \frac{0}{1} \).
—
💡 Key Concept
Zero can be written as:
\[
\frac{0}{q}, \quad \text{where } q \ne 0
\]
Hence, 0 is always a rational number.