Express each of the following as a Roman numeral:
Question 1:
(i) 2
(ii) 8
(iii) 14
(iv) 29
(v) 36
(vi) 43
(vii) 54
(viii) 61
(ix) 73
(x) 81
(xi) 91
(xii) 95
(xiii) 99
(xiv) 105
(xv) 114
Solution:
We may write these numbers as given below:
(i) 2 = II
(ii) 8 = (5 + 3) = VIII
(iii) 14 = (10 + 4) = XIV
(iv) 29 = (10 + 10 + 9) = XXIX
(v) 36 = (10 + 10 + 10 + 6) = XXXVI
(vi) 43 = (50 – 10) + 3 = XLIII
(vii) 54 = (50 + 4) = LIV
(viii) 61 = (50 + 10 + 1) = LXI
(ix) 73 = (50 + 10 + 10 + 3) = LXXIII
(x) 81 = (50 + 10 + 10 + 10 + 1) = LXXXI
(xi) 91 = (100 – 10) + 1 = XCI
(xii) 95 = (100 – 10) + 5 = XCV
(xiii) 99 = (100 – 10) + 9 = XCIX
(xiv) 105 = (100 + 5) = CV
(xv) 114 = (100 + 10) + 4 = CXIV
Question 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:
We may write these numbers in Roman numerals as follows:
(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
Question 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:
We can write the given Roman numerals in Hindu-Arabic numerals as follows:
(i) XXVII = 10 + 10 + 7 = 27
(ii) XXXIV = 10 + 10 + 10 + 4 = 34
(iii) XLV = (50 – 10) + 5 = 45
(iv) LIV = 50 + 4 = 54
(v) LXXIV = 50 + 10 + 10 + 4 = 74
(vi) XCI = (100 – 10) + 1 = 91
(vii) XCVI = (100 – 10) + 6 = 96
(viii) CXI = 100 + 10 + 1 = 111
(ix) CLIV = 100 + 50 + 4 = 154
(x) CCXXIV = 100 + 100 + 10 + 10 + 4 = 224
(xi) CCCLXV = 100 + 100 + 100 + 50 + 10 +5 = 365
(xii) CDXIV = (500 – 100) + 10 + 4 = 414
(xiii) CDLXIV = (500 – 100) + 50 + 10 + 4 = 464
(xiv) DVI = 500 + 6 = 506
(xv) DCCLXVI = 500 + 100 + 100 + 50 + 10 + 6 = 766
Question 4:
Show that each of the following is meaningless. Give reason in each case.
(i) VC
(ii) IL
(iii) VVII
(iv) IXX
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 V, L and D are never repeated.
(iv) IXX is wrong because X (ten) must be placed before IX (nine).
OBJECTIVE QUESTIONS
Mark against the correct answer in each of the following:
Question 1:
The place value of 6 in the numeral 48632950 is
(a) 6
(b) 632950
(c) 600000
(d) 486
Solution:
Option c is correct.
Place value of 6 = 6 lakhs = (6 x 100000) = 600000
Question 2:
The face value of 4 in the numeral 89247605 is
(a) 4
(b) 40000
(c) 47605
(d) 8924
Solution:
Option a is correct.
The face value of a digit remains as it is irrespective of the place it occupies in the place value chart. Thus, the face value of 4 is always 4 irrespective of where it may be.
Question 3:
The difference between the place value and the face value of 5 in the numeral 78653421 is
(a) 53416
(b) 4995
(c) 49995
(d) none of these
Solution:
Option c is correct.
Place value of 5 = 5 x 10000 = 50000
Face value of 5 = 5
Therefore, Required difference = 50000 – 5 = 49995
Question 4:
The smallest counting number is
(a) 0
(b) 1
(c) 10
(d) none of these
Solution:
Option b is correct.
The smallest counting number is 1.
Question 5:
How many 4-digit numbers are there?
(a) 8999
(b) 9000
(c) 8000
(d) none of these
Solution:
Option b is correct.
The largest four-digit number = 9999
The smallest four-digit number = 1000
Total number of all four-digit numbers = (9999 – 1000) + 1
= 8999 + 1 = 9000
Question 6:
How many 7-digit numbers are there?
(a) 8999999
(b) 9000000
(c) 1000000
(d) none of these
Solution:
Option b is correct.
The largest seven-digit number = 9999999
The smallest seven-digit number = 1000000
Total number of seven-digit numbers = (9999999 – 1000000) + 1
= 8999999 + 1 = 9000000
Question 7:
How many 8-digit numbers are there?
(a) 99999999
(b) 89999999
(c) 90000000
(d) none of these
Solution:
Option c is correct.
The largest eight-digit number = 99999999
The smallest eight-digit number = 10000000
Total number of eight-digit numbers = (99999999 – 10000000) + 1
= 89999999 + 1 = 90000000
Question 8:
What comes just before 1000000?
(a) 99999
(b) 999999
(c) 9999999
(d) none of these
Solution:
Option b is correct.
The number just before 1000000 is 999999 (i.e., 1000000 – 1)
Question 9:
Which of the following is not meaningful?
(a) VX
(b) XV
(c) XXV
(d) XXXV
Solution:
Option a is correct.
V, L and D are never subtracted. Thus VX is wrong.
Question 10:
Which of the following is not meaningful?
(a) CI
(b) CII
(c) IC
(d) XC
Solution:
Option c is correct.
I can be subtracted from V and X only. Thus, IC is wrong.
Question 11:
Which of the following is not meaningful?
(a) XIV
(b) XVV
(c) XIII
(d) XXII
Solution:
Option b is correct.
V, L and D are never repeated. Thus XVV is meaningless.
