Write each of the following as a Hindu - Arabic numeral : (i) XXVII (ii) XXXIV (iii) XLV (iv) LIV (v) LXXIV (vi) XCI (vii) XCVI (viii) CXI (ix) CLIV (x) CCXXIV (xi) CCCLXV (xii) CDXIV (xiii) CDLXIV (xiv) DVI (xv) DCCLXVI

Answer

To convert the given Roman numerals into Hindu-Arabic numerals, we will follow the rules of Roman numeral conversion. Here are the step-by-step solutions for each numeral:

### Step-by-Step Solutions:

1. **XXVII**
- X = 10 (2 times) → 10 + 10 = 20
- V = 5
- I = 1 (2 times) → 1 + 1 = 2
- Total: 20 + 5 + 2 = **27**

2. **XXXIV**
- X = 10 (3 times) → 10 + 10 + 10 = 30
- IV = 4 (5 - 1)
- Total: 30 + 4 = **34**

3. **XLV**
- L = 50
- X = 10 (to the left of L, so subtract) → 50 - 10 = 40
- V = 5
- Total: 40 + 5 = **45**

4. **LIV**
- L = 50
- I = 1 (to the left of V, so subtract) → 5 - 1 = 4
- Total: 50 + 4 = **54**

5. **LXXIV**
- L = 50
- X = 10 (2 times) → 10 + 10 = 20
- IV = 4
- Total: 50 + 20 + 4 = **74**

6. **XCI**
- C = 100
- X = 10 (to the left of C, so subtract) → 100 - 10 = 90
- I = 1
- Total: 90 + 1 = **91**

7. **XCVI**
- C = 100
- X = 10 (to the left of C, so subtract) → 100 - 10 = 90
- V = 5
- I = 1
- Total: 90 + 5 + 1 = **96**

8. **CXI**
- C = 100
- X = 10
- I = 1
- Total: 100 + 10 + 1 = **111**

9. **CLIV**
- C = 100
- L = 50
- IV = 4
- Total: 100 + 50 + 4 = **154**

10. **CCXXIV**
- C = 100 (2 times) → 100 + 100 = 200
- XX = 20
- IV = 4
- Total: 200 + 20 + 4 = **224**

11. **CCCLXV**
- C = 100 (3 times) → 100 + 100 + 100 = 300
- L = 50
- X = 10
- V = 5
- Total: 300 + 50 + 10 + 5 = **365**

12. **CDXIV**
- D = 500
- C = 100 (to the left of D, so subtract) → 500 - 100 = 400
- X = 10
- IV = 4
- Total: 400 + 10 + 4 = **414**

13. **CDLXIV**
- D = 500
- C = 100 (to the left of D, so subtract) → 500 - 100 = 400
- L = 50
- X = 10
- IV = 4
- Total: 400 + 50 + 10 + 4 = **464**

14. **DVI**
- D = 500
- V = 5
- I = 1
- Total: 500 + 5 + 1 = **506**

15. **DCCLXVI**
- D = 500
- CC = 200
- L = 50
- X = 10
- V = 5
- I = 1
- Total: 500 + 200 + 50 + 10 + 5 + 1 = **766**

### Summary of Hindu-Arabic Numerals:
- XXVII = 27
- XXXIV = 34
- XLV = 45
- LIV = 54
- LXXIV = 74
- XCI = 91
- XCVI = 96
- CXI = 111
- CLIV = 154
- CCXXIV = 224
- CCCLXV = 365
- CDXIV = 414
- CDLXIV = 464
- DVI = 506
- DCCLXVI = 766