To convert the Roman numerals to Hindu-Arabic numerals, we will follow the values assigned to each Roman numeral:
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000
Now, let's solve each part step by step:
### (i) XXIV
1. **Identify the values**: X = 10, X = 10, I = 1, V = 5
2. **Calculate**:
- XX = 10 + 10 = 20
- IV = 5 - 1 = 4
- Total = 20 + 4 = 24
3. **Result**: XXIV = 24
### (ii) XLVI
1. **Identify the values**: X = 10, L = 50, V = 5, I = 1
2. **Calculate**:
- XL = 50 - 10 = 40
- VI = 5 + 1 = 6
- Total = 40 + 6 = 46
3. **Result**: XLVI = 46
### (iii) LXXXVI
1. **Identify the values**: L = 50, X = 10, X = 10, X = 10, V = 5, I = 1
2. **Calculate**:
- L = 50
- XXX = 10 + 10 + 10 = 30
- VI = 5 + 1 = 6
- Total = 50 + 30 + 6 = 86
3. **Result**: LXXXVI = 86
### (iv) XCIX
1. **Identify the values**: X = 10, C = 100, I = 1, V = 5
2. **Calculate**:
- XC = 100 - 10 = 90
- IX = 5 - 1 = 4
- Total = 90 + 9 = 99
3. **Result**: XCIX = 99
### (v) CLXVI
1. **Identify the values**: C = 100, L = 50, X = 10, V = 5, I = 1
2. **Calculate**:
- C = 100
- L = 50
- X = 10
- VI = 5 + 1 = 6
- Total = 100 + 50 + 10 + 6 = 166
3. **Result**: CLXVI = 166
### (vi) CCXXVI
1. **Identify the values**: C = 100, C = 100, X = 10, X = 10, V = 5, I = 1
2. **Calculate**:
- CC = 100 + 100 = 200
- XX = 10 + 10 = 20
- VI = 5 + 1 = 6
- Total = 200 + 20 + 6 = 226
3. **Result**: CCXXVI = 226
### (vii) CCCXL
1. **Identify the values**: C = 100, C = 100, C = 100, X = 10, L = 50
2. **Calculate**:
- CCC = 100 + 100 + 100 = 300
- XL = 50 - 10 = 40
- Total = 300 + 40 = 340
3. **Result**: CCCXL = 340
### (viii) CDXLVI
1. **Identify the values**: C = 100, D = 500, X = 10, L = 50, V = 5, I = 1
2. **Calculate**:
- CD = 500 - 100 = 400
- XL = 50 - 10 = 40
- VI = 5 + 1 = 6
- Total = 400 + 40 + 6 = 446
3. **Result**: CDXLVI = 446
### Final Results:
- (i) XXIV = 24
- (ii) XLVI = 46
- (iii) LXXXVI = 86
- (iv) XCIX = 99
- (v) CLXVI = 166
- (vi) CCXXVI = 226
- (vii) CCCXL = 340
- (viii) CDXLVI = 446
