5th Class Mathematics Roman numerals Rules for Using Symbols

    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

 

Answer: (c)  

 

 

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  

 

Answer: (b)  

 

 

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  

 

Answer: (a)  

 

 

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  

 

Answer: (d)  

 

 

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  

 

Answer: (b)