Question Bank — A Story of Numbers

Section A — MCQs (10 questions, 1 mark each)

1. Which of the following is the correct sequence of landmark numbers in the Egyptian number system?
   (a) 1, 5, 25, 125
   (b) 1, 10, 100, 1000
   (c) 1, 2, 4, 8
   (d) 1, 60, 3600, 216000

2. The Bakhshali manuscript is associated with:
   (a) The first use of Roman numerals
   (b) The first known written use of ten digits including zero (as a dot)
   (c) The invention of tally marks on bones
   (d) The spread of numbers to Europe by Fibonacci

3. In the Roman number system, which symbol represents the landmark number 50?
   (a) L
   (b) C
   (c) D
   (d) X

4. The Gumulgal people of Australia formed number names by counting in groups of:
   (a) 5
   (b) 10
   (c) 2
   (d) 20

5. Assertion (A): The Hindu number system is a place-value system with a symbol for zero that can be used as both a placeholder and a number.
   Reason (R): This allows any number to be written unambiguously using only ten symbols.
   (a) Both A and R are true and R is the correct explanation of A.
   (b) Both A and R are true but R is not the correct explanation of A.
   (c) A is true but R is false.
   (d) A is false but R is true.

6. Which civilisation independently developed a place-value system that used a seashell-shaped symbol for zero?
   (a) Mesopotamian
   (b) Mayan
   (c) Chinese
   (d) Egyptian

7. Assertion (A): In a base-n number system the landmark numbers are successive powers of n.
   Reason (R): This property makes multiplication of landmark numbers result in another landmark number.
   (a) Both A and R are true and R is the correct explanation of A.
   (b) Both A and R are true but R is not the correct explanation of A.
   (c) A is true but R is false.
   (d) A is false but R is true.

8. The rod numerals of the Chinese system are an example of a:
   (a) Base-5 system without zero
   (b) Base-10 place-value system
   (c) Tally-mark system
   (d) Roman-style landmark system

9. The Mesopotamian (Babylonian) number system is also called:
   (a) Decimal system
   (b) Sexagesimal system
   (c) Vigesimal system
   (d) Binary system

10. Which feature is common to both the Mesopotamian and Mayan systems but absent in the earliest Roman system?
    (a) Use of a placeholder symbol for zero
    (b) Use of body parts for counting
    (c) Counting only in groups of two
    (d) Use of sticks as numerals

Section B — Very Short Answer (6 questions, 2 marks each)

1. State two limitations of representing numbers solely by tally marks or sticks.
2. Write the Roman numeral for 2367 and explain the grouping into landmark numbers.
3. What is a landmark number? Give one example each from the Roman and Egyptian systems.
4. How did the idea of counting in groups of a fixed size (such as 5 or 10) arise from human perception?
5. Differentiate between a base-n number system and a place-value system.
6. Why is zero described as “indispensable” in a fully developed place-value system?

Section C — Short Answer (5 questions, 3 marks each)

1. Represent 2660 in the Egyptian number system and show the grouping of landmark numbers.
2. Convert 143 into the base-5 system described in the chapter and write the numeral using the symbols given.
3. Add the following Egyptian numerals and show the regrouping steps:
   (a) 15 hundreds + 15 units
   (b) the resulting sum after regrouping.
4. Using the Gumulgal number names (urapon = 1, ukasar = 2), express 7 and perform the addition (ukasar-ukasar-ukasar-ukasar-urapon) + (ukasar-ukasar-ukasar-ukasar-urapon) without Hindu numerals.
5. State three features of the Hindu number system that make arithmetic operations easier than in the Roman system.

Section D — Long Answer (3 questions, 5 marks each)

1. Explain, with examples, how the Egyptian base-10 system and the base-5 system created in the chapter allow multiplication of any landmark number by 10 (or 5) to produce another landmark number. Illustrate with at least three products in each system.
2. Compare the Roman, Egyptian and Hindu number systems with respect to (i) use of landmark numbers, (ii) place value, and (iii) ease of performing multiplication. Give one concrete numerical example for each point.
3. “The introduction of zero as both a placeholder and a number was a turning point.” Justify this statement using the development from the Mesopotamian system to the Hindu number system. Include the contributions of Aryabhata and Brahmagupta.

Section E — Case/Source-Based (2 questions, 4 marks each)

Case 1

A museum curator wants to label an Ishango bone (≈20 000–35 000 years old) that shows 29 tally marks arranged in columns. She decides to also display equivalent representations in the Roman, Egyptian and base-5 systems.

Sub-questions:
(a) Write 29 in Roman numerals.
(b) Write 29 in Egyptian numerals.
(c) Write 29 in the base-5 system using the symbols given in the chapter.
(d) Which of the three systems uses the fewest symbols for 29 and why?

Case 2

A trader in ancient Mesopotamia records 3605 on a clay tablet using the sexagesimal place-value system.

Sub-questions:
(a) Show the grouping of 3605 into powers of 60.
(b) Draw/write the Mesopotamian numeral for 3605 (with correct spacing).
(c) If the same quantity were written without a placeholder symbol, what ambiguity could arise?
(d) How would the Hindu number system represent the same quantity and why is it unambiguous?