RS Aggarwal 2021-2022 for Class 6 Maths Chapter 1 - Number System
EXERCISE 1G
1. Express each of the following as a Roman numeral:
Solution Solution Solution Solution
(i) 2 = II (ii) 8 = VIII (iii) 14 = XIV (iv) 29 = XXIX
(v) 36 = XXXVI (vi) 43 = XLIII (vii) 54 = LIV (viii) 61 = LXI
(ix) 73 = LXXIII (x) 81 = LXXXI (xi) 91 = XCI (xii) 95 = XCV
(xiii) 99 = XCIX (xiv) 105 = CV (xv) 114 = CXIV
2. 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
Solution:-
(i) 164 = (100 + 50 + 10 + 4) = CLXIV
(ii) 195 = 100 + (100 - 10) + 5 = CXCV
(iii) 226 = (100 + 100 + 10 + 10 + 6) = CCXXVI
(iv) 341= 100 + 100+ 100 + (50 -10) + 1 = CCCXLI
(v) 475 = (500 - 100) + 50 + 10 + 10 + 5 = CDLXXV
(vi) 596 = 500 + (100 - 10) + 6 = DXCVI
(vii) 611= 500 + 100 + 11 = DCXI
(viii) 759 = 500 + 100 + 100 + 50 + 9 = DCCLIX
3. Write each of the following as a Hindu-Arabic numeral:
(i) XXVII (ii) XXXIV (iii) XLV (iv) LIV
(v) LXXIV (vi) XCI (vii) XCVI (viii) CXI
(ix) CLIV (x) CCXXIV (xi) CCCLXV (xii) CDXIV
(xiii) CDLXIV (xiv) DVI (xv) DCCLXVI
Solution:-
(i) XXVII = 10 + 10 + 5 + 1 + 1 = 27
(ii) XXXIV = 10 + 10 + 10 + (5 - 1) = 34
(iii) XLV = (50 − 10 ) + 5 = 45
(iv) LIV = 50 + (5 - 1) = 54
(v) LXXIV = 50 + 10 + 10 + (5 - 1) = 74
(vi) XCI = (100 − 10) + 1 = 91
(vii) XCVI = (100 − 10) + 5 + 1 = 96
(viii) CXI = 100 + 10 + 1= 111
(ix) CLIV = 100 + 50 + (5 - 1) = 154
(x) CCXXIV = 100 + 100 + 10 + 10 + (5 - 1) = 224
(xi) CCCLXV = 100 + 100 + 100 + 50 + 10 + 5 = 365
(xii) CDXIV = (500 − 100) + 10 + (5 - 1) = 414
(xiii) CDLXIV = (500 − 100) + 50 + 10 + (5 - 1) = 464
(xiv) DVI = 500 + 5 + 1 = 506
(xv) DCCLXVI = 500 + 100 + 100 + 50 + 10 + 5 + 1 = 766
4. Show that each of the following is meaningless. Give reason in each case:
(i) VC (ii) IL (iii) VVII (iv) ICC
Solution:-
(i) VC is wrong because V, L and D are never subtracted.
(ii) IL is wrong because I can be subtracted from V and X only.
(iii) VVII is wrong because V, L and D are never repeated.
(iv) IXX is wrong because X (ten) must be placed before IX (nine).
Hint. (i) V is never subtracted.
(ii) I can be subtracted from V and X only
(iii) V, L, D are never repeated.
(iv) IX cannot occur to the left of X.
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