RS Aggarwal Solutions Class 6 Ex 1C

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.


Practise This Question

Rina, who was getting bored while waiting for her friend Tina started playing with matchsticks. As the wait time was more, Rina makes “262226” by the time Tina reaches. Tina accidentally steps on the pattern and all the matchsticks were spread all over. Rina was upset with this and wanted to find the number of matchsticks she wasted?