Express each of the following as a Roman numeral : (i) 164 (ii) 195 (iii) 226 (iv) 341 (v) 475 (vi) 596 (vii) 611 (viii) 759

Answer

To convert the given numbers into Roman numerals, we will follow the Roman numeral system which uses combinations of letters from the Latin alphabet. The basic Roman numerals are:

- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000

Now, let's convert each number step by step.

### (i) Convert 164 to Roman Numerals
1. Start with the largest value less than or equal to 164, which is 100 (C).
2. Subtract 100 from 164: 164 - 100 = 64.
3. The next largest value is 50 (L). Subtract 50 from 64: 64 - 50 = 14.
4. The next largest value is 10 (X). Subtract 10 from 14: 14 - 10 = 4.
5. Finally, for 4, we use 5 (V) and subtract 1 (I): IV.
6. Combine all parts: C + L + X + IV = CLXIV.

**Roman numeral for 164 is CLXIV.**

### (ii) Convert 195 to Roman Numerals
1. Start with 100 (C).
2. Subtract 100 from 195: 195 - 100 = 95.
3. The next largest value is 90 (XC), which is 100 - 10.
4. Add 5 (V) to 90: 95.
5. Combine all parts: C + XC + V = CXCIV.

**Roman numeral for 195 is CXCIV.**

### (iii) Convert 226 to Roman Numerals
1. Start with 200 (CC).
2. Subtract 200 from 226: 226 - 200 = 26.
3. The next largest value is 20 (XX).
4. The next largest value is 5 (V).
5. Finally, for 1 (I).
6. Combine all parts: CC + XX + V + I = CCXXVI.

**Roman numeral for 226 is CCXXVI.**

### (iv) Convert 341 to Roman Numerals
1. Start with 300 (CCC).
2. Subtract 300 from 341: 341 - 300 = 41.
3. For 40, we use 50 (L) and subtract 10 (X): XL.
4. Finally, for 1 (I).
5. Combine all parts: CCC + XL + I = CCCXLI.

**Roman numeral for 341 is CCCXLI.**

### (v) Convert 475 to Roman Numerals
1. Start with 500 (D).
2. Subtract 100 (C) from 500: 500 - 100 = 400.
3. Add 50 (L): 450.
4. Add 20 (XX): 470.
5. Finally, add 5 (V).
6. Combine all parts: D - C + L + XX + V = CDLXXV.

**Roman numeral for 475 is CDLXXV.**

### (vi) Convert 596 to Roman Numerals
1. Start with 500 (D).
2. Subtract 100 (C) from 500: 500 - 100 = 400.
3. For 90, we use 100 (C) and subtract 10 (X): XC.
4. Finally, for 6 (VI).
5. Combine all parts: D + XC + VI = DXCVI.

**Roman numeral for 596 is DXCVI.**

### (vii) Convert 611 to Roman Numerals
1. Start with 500 (D).
2. Add 100 (C): 600.
3. Finally, for 11 (XI).
4. Combine all parts: D + C + XI = DCXI.

**Roman numeral for 611 is DCXI.**

### (viii) Convert 759 to Roman Numerals
1. Start with 500 (D).
2. Add 200 (CC): 700.
3. Add 50 (L): 750.
4. Finally, for 9 (IX).
5. Combine all parts: D + CC + L + IX = DCCLIX.

**Roman numeral for 759 is DCCLIX.**

### Summary of Roman Numerals
- 164 = CLXIV
- 195 = CXCIV
- 226 = CCXXVI
- 341 = CCCXLI
- 475 = CDLXXV
- 596 = DXCVI
- 611 = DCXI
- 759 = DCCLIX