Which of the following numbers can be represented as non-terminating repeating decimals ?

Options

A. `39//24`
B. `3//16`
C. `3//11`
D. `137//25`

Answer

To determine which of the given numbers can be represented as non-terminating repeating decimals, we will analyze each option step by step.

### Step 1: Understand the concept of non-terminating repeating decimals
Non-terminating repeating decimals are decimals that go on forever but have a repeating pattern. For example, \(0.333...\) (which is \( \frac{1}{3} \)) is a non-terminating repeating decimal because the digit '3' repeats indefinitely.

### Step 2: Analyze each option

1. **Option 1: \( \frac{39}{24} \)**
- Perform the division:
\[ 39 \div 24 = 1.625 \]
- This is a terminating decimal because it ends after three decimal places.

2. **Option 2: \( \frac{3}{16} \)**
- Perform the division:
\[ 3 \div 16 = 0.1875 \]
- This is also a terminating decimal as it ends after four decimal places.

3. **Option 3: \( \frac{3}{11} \)**
- Perform the division:
\[ 3 \div 11 = 0.272727... \]
- This is a non-terminating repeating decimal because the digits '27' repeat indefinitely.

4. **Option 4: \( \frac{137}{25} \)**
- Perform the division:
\[ 137 \div 25 = 5.48 \]
- This is a terminating decimal because it ends after two decimal places.

### Step 3: Conclusion
From the analysis:
- Option 1: Terminating
- Option 2: Terminating
- Option 3: Non-terminating repeating
- Option 4: Terminating

Thus, the only number that can be represented as a non-terminating repeating decimal is **Option 3: \( \frac{3}{11} \)**.

---