Unit Test (Solutions): A Story of Numbers | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: Which Roman numeral represents 50?
a) V
b) X
c) L
d) C
Answer: c) L

Q2: How is the number 27 written in Roman numerals?
a) XVII
b) XXVII
c) XXXII
d) XLVII
Answer: b) XXVII

Q3: Which major drawback did the Egyptian number system face?
a) It could not represent zero
b) It required infinite symbols for large numbers
c) It was not based on powers of 10
d) It could not be used for trade
Answer: b) It required infinite symbols for large numbers

Q4: In the Gumulgal system, the number 5 was represented as:
a) 2 + 2 + 1
b) 2 + 2 + 2
c) 2 × 2 + 2
d) 2 + 3
Answer: a) 2 + 2 + 1

Q5: The Egyptian system was based on landmark numbers that were multiples of:
a) 2
b) 5
c) 10
d) 20
Answer: c) 10

Q6. Add: LXVII + XLIX

Sol: Step 1: LXVII = 67, XLIX = 49 → 67 + 49 = 116
Step 2: 116 in Roman: C + X + VI = CXVI

Q7:  Add the following base-5 numerals: ⬤ ⬡ ⬡ ■ ▲ + ○ ⬡ ■ ■ ▲ ▲

Q8: How would the Mesopotamians have written 30, 75, 360?

• 30 = 3 × 10

• 75 = 60 + 15

• 360 = 6 × 60

Q9: Express the number 777 in the base-5 symbolic system.

Sol: Largest ≤ 777 is 625 → 777 − 625 = 152
Next ≤ 152 is 125 → 152 − 125 = 27
Next ≤ 27 is 25 → 27 − 25 = 2
Next ≤ 2 is 1+1

So: 625 + 125 + 25 + 1 + 1
Symbols: ⬤ ○ ⬡ ▲ ▲

Q10: Write Mesopotamian symbol representation for each number.

(i) 92
(ii) 371
(iii) 602

Q11. Represent the following numbers in the Egyptian system:

(i) 72,345
(ii) 49,999
(iii) 12,406

Q12: Represent the following numbers in the Roman system:

(i) 1776
Sol: 1000 + 700 + 70 + 6 = M + DCC + LXX + VI
Answer: MDCCLXXVI

(ii) 2421
Sol: 2000 + 400 + 20 + 1 = MM + CD + XX + I
Answer: MMCDXXI

(iii) 3999
Sol: 3000 + 900 + 90 + 9 = MMM + CM + XC + IX
Answer: MMMCMXCIX

(iv) 864
Sol: 800 + 60 + 4 = DCCC + LX + IV
Answer: DCCCLXIV

(vv) 948

Sol: Break it down:
900 + 40 + 8 = CM + XL + VIII

Answer: CMXLVIII

Q13. Perform operations in the Gumulgal number system:

(i) (ukasar-ukasar-urapon) + (ukasar-ukasar)
Ans: (2+2+1) + (2+2) = 5 + 4 = 9
Gumulgal: ukasar-ukasar-ukasar-urapon

(ii) (ukasar-ukasar-ukasar-ukasar) − (ukasar-urapon)
Ans: (2+2+2+2) − (2+1) = 8 − 3 = 5
Gumulgal: ukasar-urapon

(iii) (ukasar-urapon) × (ukasar-ukasar-ukasar)
Ans: (2+1) × (2+2+2) = 3 × 6 = 18
Gumulgal: ukasar written 9 times

(iv) (ukasar-ukasar-ukasar-urapon) ÷ (ukasar-urapon)
Ans: (2+2+2+1) ÷ (2+1) = 7 ÷ 3 = 2 (remainder 1)
Gumulgal: ukasar remainder urapon