Which of the following is an irrational number ?

Options

A. `pi`
B. `(22)/(7)`
C. both (A) and (B)
D. Neither (A) nor (B)

Answer

To determine which of the given options is an irrational number, let's analyze each option step by step.

### Step 1: Understanding Rational and Irrational Numbers
- **Rational Numbers**: A number that can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
- **Irrational Numbers**: A number that cannot be expressed in the form \( \frac{p}{q} \). These numbers have non-terminating, non-repeating decimal expansions.

### Step 2: Analyzing Option A: \( \pi \)
- The value of \( \pi \) (approximately 3.14159...) is known to be an irrational number.
- It cannot be expressed as a fraction of two integers.

### Step 3: Analyzing Option B: \( \frac{22}{7} \)
- The fraction \( \frac{22}{7} \) is in the form \( \frac{p}{q} \) where \( p = 22 \) and \( q = 7 \).
- Since both 22 and 7 are integers and 7 is not equal to 0, \( \frac{22}{7} \) is a rational number.

### Step 4: Conclusion
- From the analysis, we find that:
- Option A (\( \pi \)) is an irrational number.
- Option B (\( \frac{22}{7} \)) is a rational number.

Thus, the correct answer to the question "Which of the following is an irrational number?" is **Option A: \( \pi \)**.