The decimal expansion of `pi`:

Options

A. is terminating
B. is non terminating are recurring
C. is non terminating and non-recurring
D. does not exist.

Answer

To find the decimal expansion of π (pi), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding π**:
- π is a mathematical constant that represents the ratio of a circle's circumference to its diameter.

2. **Identifying the Nature of π**:
- π is classified as an irrational number. This means that it cannot be expressed as a fraction of two integers.

3. **Decimal Expansion**:
- The decimal expansion of π starts with 3.
- The approximate value of π is 3.14, but it continues indefinitely without repeating.

4. **Non-Terminating and Non-Repeating**:
- Since π does not terminate (it goes on forever) and does not repeat (there is no repeating pattern in its decimal places), it is classified as non-terminating and non-repeating.

5. **Common Approximations**:
- Two common approximations for π are:
- 22/7 (which is a rational approximation)
- 3.14 (which is a decimal approximation)

6. **Conclusion**:
- Therefore, the decimal expansion of π is non-terminating and non-repeating.

### Final Answer:
The decimal expansion of π is non-terminating and non-repeating.

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