CBSE 8th Mathematics A story of Numbers - New Model Questions Papers Study Material - QB365 Set A

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Questions:

Long Answer Type Questions

11 x 5 = 55

Find the following products.

The ancient Indians likely used base-10 for the Hindu number system because humans have
10 fingers, and so we can use our fingers to count. But what If we had only 8 fingers? How would we be writing numbers then? What would the Hindu numerals look like if we were using base-8 Instead? Base 5? Try writing the base- 10 Hindu numeral 25 as base-8 and base-5 Hindu numerals, respectively. Can you write it in base-2?

Represent the following numbers using the Mayan system.
(i) 77
(ii) 100
(iii) 361
(iv) 721

Represent the following numbers in the Mesopotamian system.
(i) 63
(ii) 132
(iii) 200
(iv) 60
(V) 3605

Create your own number system of base 4, and represent numbers from 1 to 16,

Now find the following products

Add the following Egyptian numerals.

Represent the following numbers in the Egyptain system.
(i) 10458
(ii) 1023
(iii) 2660
(iv) 784
(v) 1111
(vi) 70707

Convert the following Chinese numeral into Modern (Hindu-Arabic) number system.

10.

Represent 949 using the Mayan number system.

11.

Add 2842 + 96 using the abacus.

Multiple Choice Question

8 x 1 = 8

12.

Which of the following statements is true about the Hindu number system?

(a)

It does not use zero

(b)

It is a non- positional system.

(c)

It originated in Europe.

(d)

It uses 10symbolsincluding zero.

13.

Who played an important role in spreading the Hindu numeral system to the Arab world?

(a)

Fibonacci

(b)

Aryabhatta

(c)

Al- khwarizmi

(d)

Simon Laplace

14.

Which ancient civilisation was associated with the sexagesimal number system?

(a)

Indian

(b)

Roman

(c)

Mayan

(d)

Mesopotamian

15.

What did the Mayans uses as the symbol for zero or nothing?

(a)

A spiral

(b)

A dot

(c)

A bar

(d)

A seashell

16.

In the base-5 number system, the landmark numbers are

(a)

powers of 2 and 10

(b)

multiples of 5

(c)

powers of 5

(d)

factors of 5

17.

The Roman numeral for 2367 is

(a)

MMCDLXVII

(b)

MMCCCXLVII

(c)

MMCCCLXVII

(d)

MMXCCLXVII

18.

The symbol '0' was first introduced and used as a number and as a digit In which civilisation?

(a)

Roman

(b)

Egyptian

(c)

Indian

(d)

Mesopotamian

19.

Which of the following was one of the earliest ways humans kept count?

(a)

Writing on paper.

(b)

Counting on abacuses.

(c)

Using tally marks or notches on bones.

(d)

Using Roman numerals.

Fill up / 1 Marks

8 x 1 = 8

20.

A number system in which all landmark numbers are powers of n, is called a _________.

21.

The place value system assigns a value to a digit based on its _______ in the number.

22.

In the Gumulgal number system, 2 was represented by ________.

23.

The Hindu number system use ________ basic digits, including zero.

24.

In the Roman numeral system, the symbol for 1000 is __________.

25.

The Mesopotamian number system had base ________ and that's why called as______ system.

26.

The digit '0' was first used in India and represented as a _______ in the _________ manuscript.

27.

The earliest forms of counting were done using physical objects like ______,______or body parts.

Short Answer Type Questions

9 x 2 = 18

28.

Add the following Egyption numerals.

29.

Convert the following numerals into the Chinese rod numerals.
(i) 84
(ii) 307
(iii) 1926

30.

Convert the following Mayan numerals to Hindu-Arabic system.

31.

Convert the following numerals into Mesopotamian system.
(i) 43
(ii) 219
(iii) 1504

32.

Convert the following numerals into Egyptian number system.
(i) 426
(ii) 1032
(iii) 5790

33.

Use the extended Gumulgal number system (base-2 grouping) to perform the following operation without Converting to Hindu numerals.
(i) (ukasar- urapon) + (ukasar- urapon)
(ii) (ukasar- ukasar - ukasar- urapon) - (ukasar)
(iii) (ukasar- ukasar- urapon) x (urapon)
(iv) (ukasar - ukasar - ukasar - ukasar - urapon) ÷ (ukasar - urapon)

34.

Add the following Roman numerals without converting them to Hindu numerals.
(i) XXX + LXX
(ii) LX +XL
(iii) CD +D
(iv) CCLX + DCCXL

35.

Convert the following Hindu- Arabic numerals into Roman numerals.
(i) 388
(ii) 2071
(iii) 56

36.

Convert the following Roman numerals into Hindu-Arabic numerals.
(i) DXL
(ii) CMXLIV
(iii) LXXXIX

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Answers Key:

Long Answer Type Questions

11 x 5 = 55

Suppose if we had only 8-fingers then we might have adopted a base-8 system
We would have & symbols 0, 1, 2, 3, 4, 5, 6, 7 and the landmark numbers would be8⁰,8¹,8²,8³,.............
Also, if we were using base-5 system then we would have 5 symbols 0, 1, 2, 3, 4 and the landmark numbers would be 5⁰,5¹,5²,5³5⁴.
Now, we write the Hindu numeral 25 as base-8 system as follows.
25 = 3x8¹+ 1x8°
So, 25 can be written as 31, in base- & number system. Also, we write the Hindu numeral 25 as base-5 system as follows.
25 = 1x5²+ 0x5¹+ 0x5⁰
So, 25 can be written as 100, in base-5 number system. Next, in base- 2 number system,
25 = 1x2⁴ +1x2³+ 0x2² +0x2¹+ 1x2⁰
So, 25 =11001₂

(i) We have, 77
First, we write it as 77=3x 20+ 17
Now, we write the landmark numbers vertically from top to bottom, along with their count of occurrence and respective symbols as.

(ii) Do it same as part (i)

(iii) Do it same as part (i)

(iv) Do it same as part (i)

(i) We have, 63
First, we break it as
63 = 1x 60 +3
Now, we write the symbols for each digit and corresponding landmark numbers together to get the required Mesopotamian numeral.

(ii) Do it same as part (i)
Ans.

(iii) Do it same as part (i)
Ans.

(iv) Do it same as part (i)

(v) Do it same as part (i)

In a base -4 system, 4 symbols would be used that are 0, 1, 2 and 3 and the landmark numbers would be the powers of 4 that are 4⁰= 1,4¹= 4,4²= 16 and so on.
Now, representation of base-10 numbers 1-16 into base-4 numbers,

(i) We have,

(ii) We have,

(i) We have,

(ii) We have,

(i) We have, 10458
First we write it as 10458 = 10000+100 +100 +100+100+10+10 +10+10+10+1+1+1+1+1+1+1+1
= 10⁴+ 4 x 10² + 5 x 10¹ +8×10⁰
So, in Egyption system,

Here,

Now, on multiplying symbols', values with their corresponding landmark numbers and then adding, we get 1 x 10 + 7 x 10 + 5 × 10 + 9 x 1 = 1759

10.

We have, 949
First, we write it as
949 =2 x 360 + 11 x 20 + 9 x 1
Now, we write the landmark numbers vertically from top (highest place) to bottom (ones), along with their count of occurrence and respective symbols.

So, in the Mayan numerals, 949 is written as

11.

We first write
2842 = 1000+ 1000 + 100 + 100+ 100 + 100 + 100+ 100+ 100 + 100 + 10 + 10 + 10 + 10 + 1+ 1
and 96 = 10 + 10 + 10 + 10 + 10+ 10 + 10 + 10 + 10 +1 +1 +1 +1 + 1 +1
We represents these both numbers on either side of the vertical partition as shown below.

Now, we would bring together the counters along each line and if the counters exceed than 10 in any line then we would remove 10 counters from the current line and add one counter to the line representing the next higher place value.
So, we have Hence, 2842 + 96 =2938.

Multiple Choice Question

8 x 1 = 8

12.

(d)
It uses 10symbolsincluding zero.

13.

14.

(d)
Mesopotamian

15.

(d)
A seashell

16.

17.

18.

19.

Fill up / 1 Marks

8 x 1 = 8

20.

base n-system

21.

position

22.

ukasar

23.

24.

25.

60, sexagesimal

26.

dot, Bakhshali

27.

sticks, pebbles

Short Answer Type Questions

9 x 2 = 18

28.

(i) We have,

(ii) We have,

29.

(i) We have, 84 =8 x 10 + 1 x 4
Now, we write the Chinese symbols corresponding to each digit by identifying Zongs and Hong. Here,

So, 84 in the Chinese number system is written as

(ii) Do it same as part (i)

(iii) Do it same as part (i)

30.

So, number = 20 x 13 + 0 x 1 = 260

So, the required Hindu numeral
=18 x 360 + 20 x 1+ 0×1
= 6500

31.

(i) We have, 43 = 1 × 43
Then, in Mesopotamian numerals,

(ii) We have, 219 = 3 x 60 +39 Then, in Mesopotamian numerals,

(iii) We have, 1504 = 25 X 60 + 4 Then, in Mesopotamian numerals,

32.

(i) We first write 426 as
426 = 100+ 100+100 + 100 + 10 + 10 + 1+ 1 + 1 + 1 + 1 + 1
Then, in Egyptian numerals

(ii) We first write 1032 as
1032 = 1000 + 10+10 + 10 +1+1
Then, in Egyptian numerals,

(iii) We first writ 5790 as
5790 =5x 1000+7x100 +9×10
Then, in Egyptian numerals,

33.

(i) We have, (ukasar- urapon) + (ukasar- urapon) = ukasar - ukasar - ukasar
(ii) We have, (ukasar - ukasar - ukasar - urapon) - (ukasar) = ukasar - ukasar -urapon
(iii) We have, (ukasar - ukasar - urapon) x (urapon) = ukasar - ukasar - urapon
(iv) We have, (ukasar - ukasar - ukasar - ukasar - urapon) ÷ (ukasar - urapon)
= (ukasar - urapon - ukasar - urapon - ukasar - urapon) ÷ (ukasar - urapon)
= ukasar - urapon

34.

(i) We have,

(ii) We have,

(iii) We have,

(iv) We have,

35.

(i) We have, 388 = 100 + 100+ 100 + 50+ 10 +10 + 10 + 5 + 1 + 1 + 1
Then, in Roman numerals, 388 =CCCLXXXVIII
(ii) We have, 2071= 1000 + 1000+50 + 10+ 10 + 1
Then, in Roman numerals, 2071 =MMLXXI
(iii) We have, 56 = 50 + 5 + 1
Then, in Roman numerals, 56 = LVI

36.

(i) We have, DXL
We know, D = 500
XL=50-10 = 4
So, DXL= 500 + 40 =540
(ii) We have, CMXLIV
We know, CM= 1000- 100 = 900
XL= 50 -10 = 40
IV = 5 - 1 = 4
So, CMXLIV= 900+ 40+4=944
(iii) We have, LXXXIX
We know, L= 50
XXX=30
IX=10-1=9
So, LXXXIX= 50 + 30 + 9=89

CBSE 8th Mathematics A story of Numbers - New Model Questions Papers Study Material - QB365 Set A

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Std: 8th Standard CBSE - Mathematics

chapter: A story of Numbers - New - Model Questions Papers

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Questions:

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Answers Key:

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