Without actual division, find which of the following rational numbers have terminating decimal representation :
`(i)(5)/(32)," "(ii)(3)/(320)," "(iii)(7)/(24)`

Explanation

To determine which of the given rational numbers have a terminating decimal representation, we need to analyze the denominators of each fraction after simplifying them. A rational number has a terminating decimal representation if the denominator (after simplification) can be expressed in the form of \(2^m \times 5^n\), where \(m\) and \(n\) are non-negative integers.

Let's analyze each of the given fractions step by step:

### Step 1: Analyze the first fraction \( \frac{5}{32} \)

1. **Factor the denominator**:
- The denominator is \(32\).
- We can express \(32\) as \(2^5\).

2. **Check the form**:
- Since \(32 = 2^5\), it can be expressed in the form \(2^m\) (where \(m = 5\)) and \(5^n\) (where \(n = 0\)).
- Thus, the denominator is in the form \(2^m \times 5^n\).

3. **Conclusion**:
- Therefore, \( \frac{5}{32} \) has a terminating decimal representation.

### Step 2: Analyze the second fraction \( \frac{3}{320} \)

1. **Factor the denominator**:
- The denominator is \(320\).
- We can express \(320\) as \(2^6 \times 5^1\).

2. **Check the form**:
- Since \(320 = 2^6 \times 5^1\), it is also in the form \(2^m \times 5^n\) (where \(m = 6\) and \(n = 1\)).

3. **Conclusion**:
- Therefore, \( \frac{3}{320} \) has a terminating decimal representation.

### Step 3: Analyze the third fraction \( \frac{7}{24} \)

1. **Factor the denominator**:
- The denominator is \(24\).
- We can express \(24\) as \(2^3 \times 3^1\).

2. **Check the form**:
- The denominator \(24\) contains a factor of \(3\), which means it cannot be expressed solely in the form \(2^m \times 5^n\).

3. **Conclusion**:
- Therefore, \( \frac{7}{24} \) does not have a terminating decimal representation.

### Final Summary

- **Terminating decimals**:
- \( \frac{5}{32} \) (terminating)
- \( \frac{3}{320} \) (terminating)

- **Non-terminating decimal**:
- \( \frac{7}{24} \) (non-terminating)