Which of the following is the decimal expansions of a irrational number `

Options

A. `4.561`
B. `0.bar(12)`
C. `5.010010001...`
D. `6.03`

Explanation

To determine which of the given options represents the decimal expansion of an irrational number, we need to understand the characteristics of irrational numbers.

### Step-by-Step Solution:

1. **Understand the Definition of Irrational Numbers**:
- Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Their decimal expansions are non-terminating and non-repeating.

2. **Analyze Each Option**:
- **Option 1: 4.561**
- This is a terminating decimal (it ends after three decimal places).
- **Conclusion**: Not an irrational number.

- **Option 2: 0.12 bar (0.121212...)**
- This is a repeating decimal (the digits "12" repeat indefinitely).
- **Conclusion**: Not an irrational number.

- **Option 3: 5.01001... (with 0001 repeating)**
- This is also a repeating decimal (the digits "0001" repeat indefinitely).
- **Conclusion**: Not an irrational number.

- **Option 4: 6.03**
- This is a terminating decimal (it ends after two decimal places).
- **Conclusion**: Not an irrational number.

3. **Identify the Correct Option**:
- After analyzing all the options, we find that none of the options provided are non-terminating and non-repeating. However, if we consider the closest option that does not repeat and does not terminate, we can conclude that none of the options represent an irrational number.

### Final Conclusion:
- Based on the analysis, none of the given options represent the decimal expansion of an irrational number.