## Rules for Using Symbols

Category : 5th Class

### Rules for Using Symbols

Rule 1: When a symbol is repeated, its value is multiplied as many times as the symbol repeated.

II = 1 x 2 = 2,

III = 1 x 3 = 3,

XX = 10 x 2 = 20,

XXX = 10 x 3 = 30.

Note: A symbol cannot be repeated more than 3 times.

50 cannot be written as XXXXX.

Rule 2: The symbols whose value are power of 10 can be repeated. In other word the symbols, I, X, C, M can be repeated.

XXX = 30 , MM = 2000

Rule 3: The symbols whose value are either 5 or product of 5 and a power of 10 cannot be repeated. In other words V, L, and D cannot be repeated.

It is wrong to write LL for 100.

Rule 4: If a symbol of smaller value is right to the symbol of greater value, their values are added.

VI = 5 + 1 = 6, XV = 15, LX = 50 + 10 = 60.

Rule 5: If a symbol of smaller value is left to the symbol of greater value, their difference is the resulting value.

IV = 5 - 1 = 4, IX = 10 - 1 = 9.

Rule 6: The symbols whose value are either 5 or product of 5 and a power of 10 never subtracted. In other word V, L, and D are never written left to the symbol of greater value.

V cannot be written immediately left to X, L, C, D, and M; L can be written immediately left to the C, D, and M; D cannot be written left to the M.

Rule 7: If a symbol of smaller value comes between two symbols of larger value, its value is subtracted from the value of the symbol which is right to it.

XIX = 10+(10 - 1) = 19, L1V = 50 + (5 - 1).

Rule 8: A symbol of smaller value cannot be repeated two or more than two times left to a symbol of larger value.

30 cannot be written as XXL, similarly 8 cannot be written as IIX.

Rule 9: When a bar (horizontal line) is placed over a Roman symbol, the value of the symbol is increased by 1000 times.

$\overline{\mathbf{I}}=\mathbf{1000},\text{ }\overline{\mathbf{v}}=\mathbf{5000}.$

Look at the following table:

 I 1 XXI 21 XLI 41 LXI 61 LXXXI 81 II 2 XXII 22 XLII 42 LXII 62 LXXXII 82 III 3 XXIII 23 XLIII 43 LXIII 63 LXXXIII 83 IV 4 XXIV 24 XLIV 44 LXIV 64 LXXXIV 84 V 5 XXV 25 XLV 45 LXV 65 LXXXV 85 VI 6 XXVI 26 XLVI 46 LXVI 66 LXXXVI 86 VII 7 XXVII 27 XLVII 47 LXVII 67 LXXXVII 87 VIII 8 XXVII 28 XLVIII 48 LXVIII 68 LXXXVIII 88 IX 9 XXIX 29 XLVIII 49 LXIX 69 LXXXIX 89 X 10 XXX 30 XLIX 50 LXX 70 XC 90 XI 11 XXXI 31 LI 51 LXXI 71 XCI 91 XII 12 XXXII 32 LII 52 LXXII 72 XCII 92 XIII 13 XXXIII 33 LIII 53 LXXIII 73 XCIII 93 XIV 14 XXXIV 34 LIV 54 LXXIV 74 XCIV 94 XV 15 XXXV 35 LV 55 LXXV 75 XCV 95 XVI 16 XXXVI 36 LVI 56 LXXVI 76 XCVI 96 XVII 17 XXXVII 37 LVII 57 LXXVII 77 XCVII 97 XVIII 18 XXXVIII 38 LVIII 58 LXXVIII 78 XCVIII 98 XIX 19 XXXIX 39 LIX 59 LXXIX 79 XCIX 99 XX 20 XL 40 LX 60 LXXX 80 C 100 D 500 M 1000

Write the Roman numeral for 317.

Explanation

317 = 300 + 10 +7

And 300 = CCC, 10 = X, 7 = VII

Thus 317 = CCCXVII.

Write the Roman numeral for 548.

Explanation

548 = 500 + 40 + 8 .

And 500 = D, 40 = XL(XXXX can not be written  for 40), 8 = Vlll.

Find the value of $\overline{\text{XIV}}.$

Explanation

XIV =24, XIV = 24000.

Arrange the following in ascending order:

LXIX, XXIX, XLVII, CLIV, XCIX

Explanation

LXIX = 69, XXIX =29, XLVII = 47, CLIV = 154, XCIX = 99

Thus XXIX, XLVII, LXIX, XCIX, CLIV

• MDCLXVI is the smallest Roman numeral in which each of the symbols occurs.
• MDCLXVI is the largest Roman numeral in which each of symbols occurs.

• I, X, L, C, D, and M are seven symbols which are used to write any Roman numeral.
• No symbols can be repeated more than 3 times.
• Symbols like I, X, C and M can be repeated.
• Symbols like V, L and D cannot be repeated.
• If a symbol of smaller value is right to the symbol of greater value, their values are added.
• If a symbol of smaller value is left to the symbol of greater value, their difference is the resulting value.

Which one of the following Roman numerals is correct for 745?

(a) CCCMLXV

(b) DCCLXV

(c) DCCXLV

(d) DMXLV

(e) None of these

Amelia made a mistake while writing Roman numeral for 445. She wrote CDXIV. How will you correct themistake

(a) C should be replaced by L

(b) I should be replaced by L

(c) I should be replaced by M

(d) X should be replaced by C

(e) None of these

For which one of the following numbers, each Roman symbol used exactly once?

(a) 1666

(b) 1999

(c) 1990

(d) 1000

(e) None of these

XL represents a number. If place of the symbols is interchanged, the number will increased by:

(a) 1

(b) 5

(c) 10

(d) 20

(e) None of these

Smallest 3 digit number is subtracted from smallest 4 digit number. Write the result in Roman numeral.

(a) DM

(b) CM

(c) DCM

(d) MC

(e) None of these