CLASS V, Ch-2-ROMAN NUMERALS Roman Numerals We Have Been

We have been using the Hindu-Arabic numeral system so far. This is not the only system available. One of the early systems of writing numerals is the system of Roman numerals. This system is still used in many places. For example, we can see the use of Roman numerals in clocks; it is also used for classes in the school time table etc.

Roman numerals are expressed by seven letters of the alphabet. These are shown in the table below along with the number they represent. Roman Numerals Arabic Numerals I 1 V 5 X 10 L 50 C 100 D 500 M 1000

The Roman numerals: I, II, III, IV, V, VI, VII, VIII, IX, X denote 1,2,3,4,5,6,7,8,9 and 10 respectively. This is followed by XI for 11, XII for 12,... till XX for 20.

Rules of the System

The rules for the system are :

1. If a symbol is repeated, its value is added as many times as it occurs: i.e. II equals 2, XX is 20 and XXX is 30. 2. A symbol is repeated three times but not more than that. However, the symbols V, L and D are never repeated. 3. If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of greater symbol. VI = 5 + 1 = 6, XII = 10 + 2 = 12 and LXV = 50 + 10 + 5 = 65 4. If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol. IV = 5 – 1 = 4, IX = 10 – 1 = 9 XL= 50 – 10 = 40, XC = 100 – 10 = 90 5. The symbols V, L and D are never written to the left of a symbol of greater value, i.e. V, L and D are never subtracted. The symbol I can be subtracted from V and X only. The symbol X can be subtracted from L, M and C only.

Following these rules we get, 2

Arabic Roman Arabic Roman Arabic Roman Numerals Numerals Numerals Numerals Numerals Numerals 1 I 11 XI 30 XXX 2 II 12 XII 40 XL 3 III 13 XIII 50 L 4 IV 14 XIV 60 LX 5 V 15 XV 70 LXX 6 VI 16 XVI 80 LXXX 7 VII 17 XVII 90 XC 8 VIII 18 XVIII 100 C 9 IX 19 XIX 500 D 10 X 20 XX 1000 M

Let us look at an example of writing in Roman Numerals for the numbers 69 and 98.

69 =60+9 =(50+10)+9 =LX+IX = LXIX

98 =90+8 =(100–10)+8 =XC+VIII = LX IX = XCVIII

Summary

We use the Hindu-Arabic system of numerals and we have learnt another system of writing numerals, which is the Roman system.

1. Write the Roman numerals for each of the following Hindu-Arabic Numerals. (a)78 = 70+8 (first u hv to expand the number) =(50+10+10)+(5+1+1+1) (split the numbers into smaller) = L X X V I I I (use appropriate roman numerals down words) = LXXVIII (now compress them, u got the answer) (b) 189= 100+80+9 (c) 247=200+40+7 = 100+(50+10+10+10)+(10-1) =(100+100)+(50-10)+(5+1+1) = C L X X X IX = C C XL V I I = CLXXXIX = CCXLVII (d)196=100+90+6 (e) 365=300+60+5 3

=100+(100-10)+(5+1) =(100+100+100)+(50+10)+5 = C XC VI = C C C LX V = CXCVI = CCCLXV (f) 399=300+90+9 (g) 449=400+40+9 =(100+100+100)+(100-10)+(10-1) = (500-100)+(50-10)+(10-1) = C C C XC IX = CD XL IX = CCCXCIX = CDXLIX (h)495=400+90+5 (i)344=300+40+4 = (500-100) +(100-10)+5 =(100+100+100)+( 50-10)+(5-1) = CD XC V = C C C XL IV =CDXCV =CCCXLIV (j) 466=400+60+6 =(500-100)+(50+10)+(5+1) = CD LX VI = CDLXVI 2. Write the Hindu-Arabic Numerals corresponding to each of the following. (a) LXIX H T O (first u should place the roman numerals under place value) LX IX (IX is on Ones and LX is on Tens) = 50+10+ 9 (write the equivalent value of the roman numerals ) = 60 + 9 (add the value place wise, tens place then ones place ) = 69 (add and u got ur answer) SL Problem H T O equivalent value answer

B XCI XC I 90 1 91

C CXLVI C XL VI 100 40 6 146

D CXCII C XC II 100 90 2 192

E CCCLXXXV CCC LXXX V 300 80 5 385

F CCLIX CC L IX 200 50 9 259

G CCXCVI CC XC VI 200 90 6 296

H CXCVI C XC VI 100 90 6 196

I CCLXVI CC LX VI 200 60 6 266

J CCCXIII CCC X III 300 10 3 313

3. Which of the following are meaningless: Sl.No. Problems Meaningless Cause a) IC yes I can be subtracted from V and X only b) CI no 101=100+1=CI 4

c) IL yes I can be subtracted from V and X only d) LI no 51=50+1=LI e) VC yes V,L,D are never subtracted f) CV no 105=100+5=CV meaningful g) CXXXXVI yes Any numeral can’t be repeated four times, XXXX h) CCCCXVI yes Any numeral can’t be repeated four times, CCCC i) LLIV yes L can’t be repeated j) CCV no 205=100+100+5=CCV meaningful

4. Compare and put the correct symbol >, < or = in the placeholder:

(a) XCIII CXIII (b) CD CCCXC (c) CCLIX CLXXXIX

= 93 113 =400 390 = 259 189 < > >

(d) CDXL CDLX (e) CXLIX CLXXXIX (f) CCXXVI CCXXIX

= 440 < 460 = 149 < 189 = 226 229 <