A rational number whose reciprocal does not exist is

Options

A. 1
B. `-1`
C. 0
D. 10

Answer

To solve the question "A rational number whose reciprocal does not exist is," we need to analyze the concept of reciprocals and identify which rational number does not have a reciprocal.

### Step-by-Step Solution:

1. **Understanding Reciprocals**:
- The reciprocal of a number \( x \) is defined as \( \frac{1}{x} \). This means that for any number \( x \), if we can find \( \frac{1}{x} \), then the reciprocal exists.

2. **Testing Rational Numbers**:
- Let's consider the rational numbers one by one to see if their reciprocals exist.

3. **Testing 1**:
- The reciprocal of \( 1 \) is \( \frac{1}{1} = 1 \). This exists.

4. **Testing -1**:
- The reciprocal of \( -1 \) is \( \frac{1}{-1} = -1 \). This also exists.

5. **Testing 0**:
- The reciprocal of \( 0 \) is \( \frac{1}{0} \). However, division by zero is undefined in mathematics. Therefore, the reciprocal of \( 0 \) does not exist.

6. **Testing 10**:
- The reciprocal of \( 10 \) is \( \frac{1}{10} \). This exists.

7. **Conclusion**:
- Among the rational numbers tested, the only number whose reciprocal does not exist is \( 0 \).

Thus, the answer is **0**.