Here are the solutions for Exercise 2.2 regarding Roman numerals
Quick Reference Guide
I = 1 | V = 5 | X = 10 | L = 50 | C = 100 | D = 500 | M = 1000
Rule: Smaller values before larger ones are subtracted (e.g., IV = 4). Smaller values after larger ones are added (e.g., VI = 6).
1. Indo-Arabic Numerals
Convert the Roman numerals to standard numbers:
- (a) XXX:
- 10 + 10 + 10 =30
- (b) XC:
- 100 - 10 = 90
- (c) L:
- 50
- (d) XL:
- 50 - 10 =40
- (e) XV:
- 10 + 5 =15
- (f) CV:
- 100 + 5 =105
- (g) CD:
- 500 - 100 =400
- (h) XLVI:
- (50 - 10) + 5 + 1 =46
- (i) M:
- 1000
- (j) CM:
- 1000 - 100 =900
2. Roman Numerals
Convert the standard numbers to Roman numerals:
- (a) 26:
- 20 + 6 = XXVI
- (b) 80:
- 50 + 30 =LXXX
- (c) 65:
- 60 + 5 = LXV
- (d) 32:
- 30 + 2 = XXXII
- (e) 59:
- 50 + 9 =LIX
- (f) 200:
- CC
- (g) 205:
- 200 + 5 =CCV
- (h) 413:
- 400 + 10 + 3 = CDXIII
- (i) 600:
- 500 + 100 = DC
- (j) 800:
- 500 + 300 = DCCC
3. Arithmetic in Roman Numerals
Calculate and provide the final answer in Roman numerals:
- (a) XII + IX:
- 12 + 9 = 21 -> XXI
- (b) C + XC:
- 100 + 90 = 190 ->CXC
- (c) D – XXXI:
- 500 - 31 = 469 -> CDLXIX
- (d) CM – CD:
- 900 - 400 = 500 ->D
- (e) XV × VI:
- 15 × 6 = 90 XC
- (f) XXI × C:
- 21 × 100 = 2100 -> MMC
- (g) M ÷ D:
- 1000 \ 500 = 2 -->II
- (h) D ÷ L:
- 500 \ 50 = 10 -> X
4. Comparisons
Fill in with >, <, or =:
- (a) 99 > XCI (99 vs 91)
- (b) M = 1000 (1000 vs 1000)
- (c) XC < 110 (90 vs 110)
- (d) DLIV < 555 (554 vs 555)
- (e) CV < 150 (105 vs 150)
- (f) MMM = 3000 (3000 vs 3000)
