How a number is written affects how we read it and calculate with it. These MCQs with answers and explanations cover Class 8 Maths, Ganita Prakash Part 1, Chapter 3: A Story of Numbers. Practise early counting methods, Roman and Egyptian numerals, landmark numbers and place value. Later questions explore base-60 and Mayan representations, zero placeholders, Chinese rod numerals and conversions to bases 8, 5 and 2.
Class 8 Maths Ganita Prakash Part 1 Chapter 3 MCQs with Answers
Set 1: Early Counting and Roman Numerals MCQs (Questions 1–5)
Q1. A herder keeps one stick for each cow. After matching each returning cow with a different stick, 3 sticks remain unmatched. What does this show?
[A]. There were only 3 cows in the herd.
[B]. All cows have returned.
[C]. 3 extra cows have returned.
[D]. 3 cows have not returned.
Q2. In the Gumulgal number system, urapon means 1 and ukasar means 2. What number is ukasar-ukasar-urapon?
[A]. 3
[B]. 4
[C]. 5
[D]. 6
Q3. Extend Gumulgal counting by adding the values of its words, with ukasar = 2 and urapon = 1. What is (ukasar-ukasar-ukasar-ukasar-urapon) − (ukasar-ukasar-ukasar)?
[A]. ukasar-urapon
[B]. urapon
[C]. ukasar
[D]. ukasar-ukasar
Q4. Which Roman numeral represents 1222?
[A]. MCCCXXII
[B]. MMCCXXII
[C]. MCCXII
[D]. MCCXXII
Set 2: Roman Arithmetic and Egyptian Numerals MCQs (Questions 6–10)
Q6. Which Roman numeral is equal to LXXXVII + LXXVIII?
[A]. CLXXV
[B]. CLXV
[C]. CXLV
[D]. CLV
Q8. In Egyptian numerals, separate symbols represent 100, 10 and 1. How many symbols are needed altogether to write 324 using the largest possible groups?
[A]. 6
[B]. 9
[C]. 8
[D]. 7
Q9. Egyptian numerals use a separate symbol for each power of 10. How many symbols are needed to write 10458 using the largest possible groups?
[A]. 18
[B]. 20
[C]. 23
[D]. 19
Q10. Which grouping correctly represents 70707 using Egyptian landmark numbers?
[A]. 7 × 10000 + 7 × 100 + 7
[B]. 7 × 10000 + 7 × 1000 + 7
[C]. 7 × 10000 + 7 × 10 + 7
[D]. 7 × 1000 + 7 × 100 + 7
Set 3: Bases and Landmark Numbers MCQs (Questions 11–15)
Q11. A base-5 system has landmark numbers 1, 5, 25 and 125. What is the next landmark number?
[A]. 625
[B]. 250
[C]. 3125
[D]. 130
Q12. In an additive base-5 system, ○ represents 125, □ represents 5 and △ represents 1. Which expression represents 137?
[A]. ○ + □ + □ + □ + △ + △
[B]. ○ + □ + △ + △
[C]. ○ + □ + □ + △ + △
[D]. ○ + □ + □ + △
Q13. Which list gives the first four landmark numbers of a base-7 system?
[A]. 0, 7, 49, 343
[B]. 1, 7, 49, 343
[C]. 1, 7, 14, 21
[D]. 1, 7, 70, 700
Q14. Five symbols, each worth 25, occur in an additive base-5 calculation. What single landmark value can replace them?
[A]. 100
[B]. 625
[C]. 30
[D]. 125
Q15. Egyptian landmark numbers are powers of 10. What is the product of the landmarks 100 and 1000?
[A]. 1000000
[B]. 10000
[C]. 100000
[D]. 1100
Set 4: Grouping and Place Value MCQs (Questions 16–20)
Q16. While adding 2907 and 43 on a decimal abacus, 7 ones and 3 ones are regrouped as 1 ten. What is the final sum?
[A]. 2940
[B]. 29410
[C]. 3000
[D]. 2950
Q17. Why does writing ever larger numbers in the Egyptian system require more kinds of symbols?
[A]. Each higher power of 10 needs its own landmark symbol.
[B]. The system has no grouping of numbers.
[C]. A symbol changes its value whenever its position changes.
[D]. Every unit must always be shown separately.
Q18. Which grouping of 640 has fewer than 60 units in each place of a base-60 system?
[A]. 6 × 60 + 40
[B]. 10 × 60 + 40
[C]. 10 × 60 + 4
[D]. 6 × 60 + 4
Q19. A base-60 numeral has 2 in the 3600-place, 5 in the 60-place and 30 in the units place. What number does it represent?
[A]. 7235
[B]. 7503
[C]. 7530
[D]. 23530
Q20. After regrouping, which expression represents 1 × 3600 + 70 × 60 + 2 with every place count smaller than 60?
[A]. 2 × 3600 + 10 × 60 + 2
[B]. 2 × 3600 + 70 × 60 + 2
[C]. 1 × 3600 + 10 × 60 + 2
[D]. 70 × 3600 + 1 × 60 + 2
Set 5: Zero Placeholders and Mayan Numerals MCQs (Questions 21–25)
Q21. In a base-60 place-value system with a zero placeholder, which counts belong in the 3600-, 60- and 1-places for 3605, in that order?
[A]. 1, 5, 0
[B]. 0, 60, 5
[C]. 1, 0, 5
[D]. 3, 6, 5
Q22. In Mayan numerals, a dot represents 1 and a bar represents 5. What is the value of a group containing two bars and one dot?
[A]. 7
[B]. 11
[C]. 15
[D]. 10
Q23. A Mayan numeral has 3 in the 20-place and 17 in the units place. What number does it represent?
[A]. 60
[B]. 317
[C]. 37
[D]. 77
Q24. A Mayan numeral has 1 in the 360-place, 0 in the 20-place and 1 in the units place. What is its value?
[A]. 381
[B]. 361
[C]. 401
[D]. 721
Q25. The Mayan landmark sequence begins 1, 20, 360. Why is this not an exact base-20 sequence?
[A]. The first landmark should be 0.
[B]. The third landmark would have to be 20 × 20 = 400.
[C]. Every landmark should be 20 more than the previous one.
[D]. A base-20 system cannot have a zero placeholder.
Set 6: Place Value and Base Conversions MCQs (Questions 26–30)
Q26. In the Chinese rod numeral for 2634, the digit 6 occupies the hundreds place. What is its contribution to the number?
[A]. 600
[B]. 6
[C]. 6000
[D]. 60
Q27. Which equation correctly shows the place values of the digits in 375?
[A]. 375 = 3 × 100 + 7 × 1 + 5 × 10
[B]. 375 = 3 + 7 + 5
[C]. 375 = 3 × 10 + 7 × 100 + 5 × 1
[D]. 375 = 3 × 100 + 7 × 10 + 5 × 1
Q28. How is the decimal number 25 written in a base-8 place-value system?
[A]. 25₈
[B]. 11001₈
[C]. 31₈
[D]. 100₈
Q29. How is the decimal number 25 written in a base-5 place-value system?
[A]. 100₅
[B]. 1000₅
[C]. 25₅
[D]. 50₅
Q30. How is the decimal number 25 written in a base-2 place-value system?
[A]. 10011₂
[B]. 11100₂
[C]. 11001₂
[D]. 10101₂
Part 1 Chapter 3: Full Chapter MCQs (Set 1)
Q31. Around how many years ago did a civilization flourish in Mesopotamia, where strange symbols were used for numbers?
[A]. 3000 years ago
[B]. 4000 years ago
[C]. 5000 years ago
[D]. 2000 years ago
Q32. According to the chapter, when did humans first have the need to count?
[A]. With the rise of modern civilization
[B]. As early as the Stone Age
[C]. After the invention of writing
[D]. During the Bronze Age
Q33. Where did the modern oral and written numbers, using digits 0 through 9, originate and develop?
[A]. Europe
[B]. China
[C]. India
[D]. Mesopotamia
Q34. What was the notation for the digit 0 in the Bakhshali manuscript (c. 3rd century CE)?
[A]. A square
[B]. A dot
[C]. A dash
[D]. A circle
Part 1 Chapter 3: Full Chapter MCQs (Set 2)
Q35. Which mathematician was the first to fully explain and do elaborate scientific computations with the Indian system of 10 symbols around 499 CE?
[A]. Fibonacci
[B]. Aryabhata
[C]. Brahmagupta
[D]. Al-Khwarizmi
Q36. How were Hindu numerals transmitted to the Arab world?
[A]. Through direct trade routes from India
[B]. By the mathematician Al-Khwarizmi around 800 CE
[C]. By the philosopher Al-Kindi around 830 CE
[D]. Both b and c
Q37. Why did European scholars call Indian numerals “Arabic numerals”?
[A]. To reflect their European perspective, as they learned them from the Arab world
[B]. Due to a mistranslation of Indian texts
[C]. Because Arab scholars preferred this term
[D]. Because they were invented in the Arab world
Q38. What are the most commonly used terminologies for the numbers we use today?
[A]. Hindu numerals, Indian numerals, Hindu-Arabic numerals
[B]. Modern numbers, Universal numbers, Decimal numbers
[C]. Counting numbers, Natural numbers, Whole numbers
[D]. Arabic numbers, Roman numbers, European numbers
Part 1 Chapter 3: Full Chapter MCQs (Set 3)
Q39. What is a one-to-one mapping in the context of counting?
[A]. Grouping objects into sets of ten
[B]. Associating each object with a unique stick, such that no two objects share the same stick
[C]. Counting objects using a sequence of sounds
[D]. Associating all objects with a single stick
Q40. What is an obvious limitation of using only the letters of the English alphabet (Method 2) to represent numbers?
[A]. It is not convenient for verbal representation.
[B]. It cannot be used to count collections having more than 26 objects.
[C]. It requires new symbols for every number.
[D]. It is difficult to write large numbers.
Q41. What are the marks cut on a surface like a bone or cave wall, used for number representation, called?
[A]. Cuneiforms
[B]. Tally marks
[C]. Pictograms
[D]. Hieroglyphs
Q42. The Gumulgal people of Australia counted in groups of which number?
[A]. 1
[B]. 5
[C]. 2
[D]. 0
Part 1 Chapter 3: Full Chapter MCQs (Set 4)
Q43. What is the human limit for immediately knowing the size of a collection at a glance, according to the chapter?
[A]. Up to 5 or more objects
[B]. Up to 10 objects
[C]. Up to 20 objects
[D]. Up to 3 objects
Q44. In the Roman number system, what new symbol is introduced to represent 50?
[A]. C
[B]. D
[C]. L
[D]. X
Q45. What tool did people using the Roman system employ to perform arithmetic operations?
[A]. Abacus
[B]. Slide rule
[C]. Counting board
[D]. Calculator
Q46. What is the defining characteristic of a base-n number system according to the chapter?
[A]. The first landmark number is 1, and every next landmark number is obtained by multiplying the current landmark number by some fixed number ‘n’.
[B]. It uses only n symbols.
[C]. It is a place value system.
[D]. Each landmark number is 10 times the previous one.
Part 1 Chapter 3: Full Chapter MCQs (Set 5)
Q47. What is the Egyptian number system classified as?
[A]. A base-20 system
[B]. A base-10 system
[C]. A base-60 system
[D]. A base-5 system
Q48. What was a key shortcoming of the Egyptian number system despite its relative efficiency?
[A]. It lacked symbols for numbers greater than 1000.
[B]. It required inventing an unending sequence of symbols for higher and higher powers of 10 for larger numbers.
[C]. Its symbols were ambiguous and easily confused.
[D]. It was difficult to represent very small numbers.
Q49. The Mesopotamian number system later became a base-60 system, also known as what?
[A]. Sexagesimal system
[B]. Binary system
[C]. Quinary system
[D]. Decimal system
Q50. What is a “positional number system” or “place value system”?
[A]. A system where symbols are placed vertically to represent a number.
[B]. A system with a base that uses the position of each symbol to determine the landmark number it is associated with.
[C]. A system that requires a new symbol for every landmark number.
[D]. A system that uses only ten symbols for all numbers.
Connect Symbols with Their Values
Write the value contributed by each symbol or position before calculating. For a base conversion, list the place values and show which positions need zero. Compare the additive grouping of Egyptian numerals with positional notation. Pay particular attention to the Mayan sequence 1, 20, 360, which differs from successive powers of 20.
