Which of the following conversions is/are incorrect?
(i) 10 decades = 1 century
(ii) 100 centuries = 1 millennium
(iii) 100 inches = 2.54 metres
(iv) 100 millimetres = 10 centimetres

Options

A. (ii) only
B. (iv) only
C. (i) and (ii) only
D. (iii) and (iv) only

Explanation

To determine which of the given conversions is incorrect, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Option (i): 10 decades = 1 century**
- A decade is 10 years.
- Therefore, 10 decades = 10 × 10 years = 100 years.
- A century is also defined as 100 years.
- Conclusion: 10 decades = 1 century is **correct**.

2. **Option (ii): 100 centuries = 1 millennium**
- A century is 100 years.
- Therefore, 100 centuries = 100 × 100 years = 10,000 years.
- A millennium is defined as 1,000 years.
- Conclusion: 100 centuries = 1 millennium is **incorrect**.

3. **Option (iii): 100 inches = 2.54 metres**
- The conversion factor states that 1 inch = 0.0254 meters.
- Therefore, 100 inches = 100 × 0.0254 meters = 2.54 meters.
- Conclusion: 100 inches = 2.54 metres is **correct**.

4. **Option (iv): 100 millimetres = 10 centimetres**
- The conversion factor states that 1 centimetre = 10 millimetres.
- Therefore, 100 millimetres = 100 ÷ 10 centimetres = 10 centimetres.
- Conclusion: 100 millimetres = 10 centimetres is **correct**.

### Final Conclusion:
- The incorrect conversion is **Option (ii): 100 centuries = 1 millennium**.