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 â€“ 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 â€“ 10) + 1 = XCI

(xii) 95 = (100 â€“ 10) + 5 = XCV

(xiii) 99 = (100 â€“ 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 â€“ 10) + 5 = CXCV

(iii) 226 = (100 + 100 + 10 + 10 + 6) = CCXXVI

(iv) 341 = 100 + 100 + 100 + (50 â€“ 10) + 1 = CCCXLI

(v) 475 = (500 â€“ 100) + 50 + 10 + 10 + 5 = CDLXXV

(vi) 596 = 500 + (100 â€“ 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 â€“ 10) + 5 = 45

(iv) LIV = 50 + 4 = 54

(v) LXXIV = 50 + 10 + 10 + 4 = 74

(vi) XCI = (100 â€“ 10) + 1 = 91

(vii) XCVI = (100 â€“ 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 â€“ 100) + 10 + 4 = 414

(xiii) CDLXIV = (500 â€“ 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 â€“ 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 â€“ 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 â€“ 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 â€“ 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 â€“ 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.