RS Aggarwal Solutions Class 6 Ex 1C

RS Aggarwal Class 6 Ex 1C Chapter 1

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

Express 16,200 as a product of powers of prime numbers in the exponential form.