Important Questions Class 8 Maths Chapter 3 A Story of Numbers

Important Questions Class 8 Maths Chapter 3 A Story of Numbers

A Story of Numbers is Chapter 3 of the Class 8 Maths book Ganita Prakash. It tells the story of how people counted and wrote numbers in different times and places. Students explore early counting systems, Egyptian, Roman, Mesopotamian, Mayan and Chinese numerals, and the Hindu-Arabic place value system we use today.

This page gives 12 important questions from Class 8 Maths Chapter 3 A Story of Numbers with step-by-step answers prepared by Extramarks experts. The questions cover early counting systems, landmark numbers, Egyptian and Roman numerals, number bases and the place value system. Solve each question on paper first and then check your working with the answer.

Q1. Why did early counting systems begin using landmark numbers such as 5, 10, or 20? Explain how these landmark values helped people represent and understand larger quantities more effectively.

Answer: Landmark numbers made counting more efficient because they acted as natural grouping points. Instead of marking each object individually, people collected items into fixed-size groups like five or ten, reducing the total number of marks needed. These groups created predictable patterns that were easier to recognise and compare. As a result, landmark numbers improved clarity, speed, and accuracy in representing large quantities.

Q2. Calculate the sum of the Egyptian numerals presented in the image below. Explain the steps involved in arriving at the final answer, including the value of each distinct Egyptian symbol shown.

Answer: Step 1: Know the value of each symbol. A single vertical stroke (∣) stands for 1 and a heel bone (∩) stands for 10.

Step 2: The first number has seven heel bones and six strokes: 7 × 10 + 6 × 1 = 70 + 6 = 76.

Step 3: The second number has six heel bones and eleven strokes: 6 × 10 + 11 × 1 = 60 + 11 = 71.

Step 4: Add the two numbers: 76 + 71 = 147.

Therefore, the sum of the given Egyptian numerals is 147.

Q3. Compare how 404 would be written in:

Egyptian (with symbols)

Roman numerals

With a zero placeholder

Answer: Egyptian: four coiled-rope symbols (each 100) followed by four strokes (||||)

Roman: CDIV

With zero: 4-0-4

Q4. Convert these Mesopotamian symbols to Hindu-Arabic numerals: 𒐕 = 1, 𒌋 = 10

If you see: 𒌋𒌋𒌋 𒐕𒐕𒐕𒐕𒐕𒐕𒐕

What number does this represent?

Answer: 𒌋𒌋𒌋 = 30

𒐕𒐕𒐕𒐕𒐕𒐕𒐕 = 7

Total = 37

Q5. Using Roman numerals, solve: XLVII + XXVIII. Express your answer in Roman numerals.

Answer: XLVII = 47

XXVIII = 28

47 + 28 = 75

75 = LXXV

Q6. Convert the decimal number

Answer:

Divide 512 by 8 repeatedly and record the remainders.

512 ÷ 8 = 64 remainder 0

64 ÷ 8 = 8 remainder 0

8 ÷ 8 = 1 remainder 0

1 ÷ 8 = 0 remainder 1

512₁₀ = 1000₈

Q7. Explain how the number 25 is represented in the Mayan number system. Describe the symbols used for each position and the reasoning behind their placement.

Answer: The Mayan system is based on 20. 25 = 1 × 20 + 5. So, one dot (for 1 group of twenty) is placed in the upper position and one bar (for 5) is placed in the lower position.

Q8. The number 3,047 is represented in Chinese rod numerals using a specific alternating pattern of 'Heng' (horizontal) and 'Zong' (vertical) symbols for its digits. Explain the rule that determines whether a 'Heng' or 'Zong' orientation is used for each place value, and illustrate this rule using the number 3,047.

Answer: In the Chinese rod numeral system, the orientation of the rods alternates with each place value to avoid ambiguity. 'Zong' (vertical) rods are used for the ones, hundreds, and ten thousands places. 'Heng' (horizontal) rods are used for the tens, thousands, and hundred thousands places. For the number 3,047:

1. The thousands place (digit 3) uses the 'Heng' orientation.

2. The hundreds place (digit 0) uses the 'Zong' orientation.

3. The tens place (digit 4) uses the 'Heng' orientation.

4. The ones place (digit 7) uses the 'Zong' orientation.

This creates the left-to-right pattern: Heng, Zong, Heng, Zong.

Q9. Why are Hindu numerals considered efficient for representing large numbers? Explain how their positional structure helps maintain clarity and reduces the need for many different symbols.

Answer: Hindu numerals are efficient because a small set of digits can represent very large values through positional arrangement. Each digit’s value changes depending on the place it occupies, so new symbols are not needed for higher numbers. This structure makes writing compact and easier to interpret, since position itself conveys meaning. As a result, calculations become simpler and representation remains clear even for large quantities.

Q10. Two cultures use positional numerals with the same symbols, but one uses base 12 and the other base 20. Explain why the same written numeral can represent drastically different quantities depending on the base.

Answer: Consider the written numeral 2 5 3.

In base 12, its value is 2 × 12² + 5 × 12 + 3 = 288 + 60 + 3 = 351

In base 20, its value is 2 × 20² + 5 × 20 + 3 = 800 + 100 + 3 = 903

The arrangement 2 5 3 looks the same, but the place values are powers of the base (12 or 20), so each position is scaled differently. The base alone changes the value.

Q11. Explain why tally marks became inefficient as numbers grew larger. Describe how early humans adapted their counting methods to overcome the limitations of simple tallies.

Answer: Tally marks became inefficient because larger quantities required long strings of strokes that were difficult to read and easy to miscount. As numbers increased, keeping track visually demanded repeated recounting, slowing down the process. To overcome this, early humans began grouping tallies into sets, such as fives or tens, which made quantities easier to recognise. This shift toward grouping led to more organised counting methods and laid the foundation for later numeral systems.

Q12. Explain the fundamental difference between the base systems of the Chinese rod numerals and the Mayan numerals. How did this difference impact the efficiency of performing calculations in each system?

Answer: The Chinese rod numeral system is a true base-10 (decimal) system, where each place value is consistently ten times the value of the place to its right. In contrast, the Mayan numeral system is a modified base-20 (vigesimal) system. The crucial difference is that in the Mayan

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