Class 08 | Ganita Prakash | Part 2 | Ch 03 A Story of Numbers | Extra Questions

Ganit Prakash | Class 8 | Maths | Ch 3 A Story of Numbers | Extra Questions

Class 8 Maths Chapter 3 Extra Questions A Story of Numbers Extra Questions Class 8

Question 1.
Evaluate the following:
(a) CXXI + XXXIV
(b) CCLXXII – LXXXIX
(c) C × IV
(d) CDLVI ÷ VIII
Solution:
(a) CXXI + XXXIV
= 121 + 34
= 155
= CLV

(b) CCLXXII – LXXXIX
= 272 – 89
= 183
= CLXXXIII

(c) IV × C = IV times C
= 4 times C
= C + C + C + C
= 400
= CD

(d) CDLVI ÷ VIII
= 456 ÷ 8
= 57
= LVII

Question 2.
Shweta and her mother went to a toy shop to buy a teddy bear. Her mother paid DCCX rupees for a toy. The shopkeeper gave them a discount of CXV rupees. So, how much did the teddy bear finally cost them?
Solution:
Price of the teddy bear = DCCX
Discount given by the shopkeeper = CXV
Therefore, the final cost of the teddy bear = DCCX – CXV
= 710 – 115
= 595
= DXCV
Thus, the cost of the teddy bear after discount is DXCV rupees.

Question 3.
Convert the following numbers in different number system as directed:
(a) 2478 in Egyptian system of notation.
(b) 5832 in the Mesopotamian number system.
(c) 1728 in Mayan Number system.
Solution:
(a) 2478 in Egyptian system of notation:
Convert the number into base-10,
2478 = 2 × 1000 + 4 × 100 + 7 × 10 + 8 × 1
= 2 × 10³ + 4 × 10² + 7 × 10¹ + 8 × 1

(b) 5832 in the Mesopotamian number system:
Convert the number into the base-60 system.
5832 = 1 × 3600 + 37 × 60 + 12
= 1 × (60)² + 37 × (60)¹ + 12 × (60)⁰

(c) 1728 in the Mayan Number system
Convert the number into the base-20 system.
1728 = 4 × 360 + 14 × 20 + 8 × 1
= 4 × (20 × 18) + 14 × (20)¹ + 8 × (20)⁰

Question 4.
Evaluate the following and convert the result into the Egyptian number system.
(a) MCCXLIX + CCCXIX
(b) 
(c) 
Solution:
(a) MCCXLIX + CCCXIX = 1249 + 319 = 1568
Convert the sum that is 1568 into the base-10 system of Egyptian,
1568 = 1 × 1000 + 5 × 100 + 6 × 10 + 8
= 1 × 10³ + 5 × 10² + 6 × 10¹ + 8 × 1

(b) This number is in the Mesopotamian number system.
Write it into the base-60 system.

= 10 × (60)¹ + 40
= 10 × 60 + 40
= 640
Now, convert into the base-10 system,
640 = 6 × 100 + 4 × 10 = 6 × (10)² + 4 × (10)¹
Now, represent it into Egyptian number system as

(c)

This number is in the Mayan number system.
Write it into base-20 system.
3 × 7200 + 17 × 360 + 8 × 20 + 0 × 1
= 21600 × 6120 + 160 + 0
= 27880
Now, to represent it into Egyptian number system, convert it into base-10 system.
27880 = 2 × 10⁴ + 7 × 10³ + 8 × 10² + 8 × 10

Question 5.
Represent the following using the Egyptian system.
(a) 231
(b) 1043
Solution:
(a) 231 = 100 + 100 + 10 + 10 + 10 + 1

(b) 1043 = 1000 + 10 + 10 + 10 + 10 + 1 + 1 + 1

Question 6.
Represent the following in the Hindu number system.


Solution:
(a) 2 × 100 + 7 × 10 + 6 × 1
= 200 + 70 + 6
= 276

(b) 4 × 1000 + 3 × 100 + 2 × 10 + 2 × 1
= 4000 + 300 + 20 + 2
= 4322

Question 7.
Represent the following using the Egyptian system.
(a) 210
(b) 1043
Solution:
(a) 210 = 3 × 60 + 3 × 10

This is written in a compact way as

Note that  is omitted.
A blank space is left in its place.

(b) 1043 = 17 × 60 + 10 + 10 + 3

This is written in a compact way as

Note that  is omitted.
Blank spaces are left in their places.

Question 8.
Represent the following in the Hindu number system.

Solution:
(a) 2 × 3600 + 1 × 60 + 2 × 10 + 3 × 1
= 7200 + 60 + 20 + 3
= 7283

(b) 3 × 3600 + 2 × 60 + 3 × 10 + 1 × 1
= 10800 + 120 + 30 + 1
= 10951

Question 9.
Represent the following using the Mayan system.
(a) 1661
(b) 1842
Solution:
(a) 1661 = 4 × 360 + 11 × 20 + 1 × 1

(b) 1842 = 5 × 360 + 2 × 20 + 2

Question 10.
Represent the following in the Hindu number system.

Solution:
(a) 3 × 360 + 6 × 20 + 0 × 1 = 1200
(b) 6 × 360 + 2 × 20 + 5 × 1 = 2205

Question 11.
Represent the following using the Chinese Number System.
(a) 3264
(b) 4758
Solution:
(a) 3264: 
(b) 4758: 

Question 12.
Represent the following in the Hindu Number System.
(a) 
(b) 
Solution:
(a) 32685
(b) 14793

Practice Questions

Question 1.
Mention three items that can be used to count using one-to-one mapping.
Solution:
Pebbles, Marbles, Sticks

Question 2.
Name three number systems that were in use in historical times.
Solution:
Mayan, Egyptian, Mesopotamian

Question 3.
Name two number systems which are in use presently.
Solution:
Hindu and Binary

Question 4.
Give an example to show how you will use letters of the alphabet (any language) as counting tokens using one-to-one mapping.
Solution:
a for 1, b for 2, …….., z for 26
aa for 27, bb for 28, ……., zz for 52
aaa for 53, bbb for 54, ……., zzz for 78,…

Question 5.
Define a number system. Give two examples.
Solution:
Number system is a way of representing numbers using digits or symbols and defining rules for operations on those numbers.
Example: Roman Number System, Hindu Number System

Question 6.
What are numerals? Give examples.
Solution:
Symbols used to write numbers, for example, 1, 2, 3,…

Question 7.
Write the following using Tally marks.
(a) 9
(b) 14
Solution:

Question 8.
Write the following in Roman numerals.
(a) 25
(b) 58
(c) 194
(d) 246
(e) 413
Solution:
(a) XXV
(b) LVIII
(c) CXCIV
(d) CCXLVI
(e) CDXIII

Question 9.
Write the following in Hindu numerals.
(a) XXXV
(b) XLVI
(c) LXXXIX
(d) CCLVIII
Solution:
(a) 35
(b) 46
(c) 89
(d) 268

Question 10.
Simplify:
(a) CLXVI + DCCXXII
(b) CCCXXXVIII – CCXXII
Solution:
(a) DCCCLXXXVIII
(b) CXVI

Question 11.
Write the following in Roman numerals.
(a) 637
(b) 481
(c) 1642
(d) 2799
Solution:
(a) DCXXXVII
(b) CDLXXXI
(c) MDCXLII
(d) MMDCCXCIX

Question 12.
Write the following in Hindu numerals.
(a) DCXLIII
(b) MDCCLXXI
(c) MDXCIV
(d) MMDCCXIII
Solution:
(a) 643
(b) 1771
(c) 1594
(d) 2713

Question 13.
Simplify:
(a) DCLX + DCCXXV
(b) DCLXVIII – CCCXII
Solution:
(a) MCCCLXXXV
(b) CCCLVI

Question 14.
Identify the features of the Hindu number system that make it efficient when compared to the Roman number system.
Solution:
‘0’ and ‘place value’

Question 15.
Give the symbol to represent 10,000 in the Egyptian system.
Solution:

Question 16.
Which number cannot be represented in the Egyptian system?
Solution:
0

Question 17.
Represent 324 in the Egyptian system.
Solution:

Question 18.
Represent  in the Hindu system.
Solution:
2212

Question 19.
Give the symbol to represent 3125 in the base 5 system.
Solution:
↑

Question 20.
Which number cannot be represented in the base 5 system?
Solution:
0

Question 21.
Represent 279 in the base 5 system.
Solution:

Question 22.
Represent  in the Hindu system.
Solution:
281

Question 23.
Find the sum: 
Solution:
625 or 

Question 24.
Add: 
Solution:
1606 or 

Question 25.
Add: 
Solution:
292 or 

Question 26.
Find the product  of and .
Solution:

Question 27.
Find the sum: 
Solution:

Question 28.
Multiply: 
Solution:

Question 29.
Multiply: 
Solution:

Question 30.
Write the landmark numbers of the Mesopotamian number system.
Solution:
1, 60, 3600, 216000

Question 31.
Represent  in Hindu number system.
Solution:
2 × 60 + 20 + 3 = 143

Question 32.
Represent 3605 in the  Mesopotamian number system.
Solution:

Question 33.
Write the landmark numbers of the Mayan number system.
Solution:
1, 20, 360, 7200, 144000

Question 34.
Write the landmark numbers of the Chinese number system.
Solution:
1, 10, 100, 1000, 10000, etc..

Question 35.
Represent  in the Hindu number system.
Solution:
361

Question 36.
Represent  in the Hindu number system.
Solution:
6472

Question 37.
Represent 721 in the  Mayan number system.
Solution:

Question 38.
Represent 2364 in Chinese number system.
Solution: