A Story of Numbers explains how humans counted, represented numbers, created number systems and finally developed place value with zero. It shows why the modern Hindu number system became powerful, compact and widely used.
Important Questions Class 8 Maths Chapter 3 help students revise one-to-one mapping, numerals, landmark numbers, Roman numerals, Egyptian numerals, base-n systems, place value systems and the role of zero. This chapter builds number sense by showing why our current number system works so efficiently.
Class 8 Maths Chapter 3 starts with Reema finding an old page filled with strange symbols. Her curiosity opens a journey through number history, from Stone Age counting to Mesopotamian, Roman, Egyptian, Mayan, Chinese and Hindu number systems.
Students learn that numbers did not always look like 0, 1, 2, 3 and so on. People once counted with sticks, body parts, tally marks, sounds and symbols. The chapter explains how humans solved one problem after another: how to count large collections, how to write numbers compactly, how to calculate efficiently, and how zero removed confusion in place value.
Key Takeaways from Class 8 Maths Chapter 3
| Topic |
What Students Must Know |
| Chapter Name |
A Story of Numbers |
| Main Idea |
Evolution of number representation |
| Core Concept |
Number systems use ordered objects, names or symbols |
| Important Method |
One-to-one mapping |
| Early Systems |
Tally marks, body-part counting, Roman numerals |
| Base Systems |
Egyptian, base-5, base-7 and base-n systems |
| Place Value Systems |
Mesopotamian, Mayan, Chinese and Hindu systems |
| Most Important Idea |
Zero as a digit, placeholder and number |
Important Questions Class 8 Maths Chapter 3 with Answers
These questions cover the main ideas of the chapter. Students should focus on definitions, examples and reasons.
Important Questions Class 8 Maths Chapter 3: Basic Concepts
Q1. What is a number system?
A number system is a standard sequence of objects, names or written symbols used for counting.
This sequence must have a fixed order. For example, the Hindu number system uses digits from 0 to 9 and place value to represent numbers.
Q2. What are numerals?
Numerals are symbols used to represent numbers in a written number system.
For example, 0, 1, 5, 36 and 193 are numerals in the Hindu number system.
Q3. Why did early humans need counting?
Early humans needed counting to track food, animals, trade goods, offerings and days.
They also counted to predict events such as seasons, full moons and new moons. Counting helped them manage daily life.
Q4. What is one-to-one mapping in counting?
One-to-one mapping means matching each object in a collection with exactly one object, mark, sound or symbol.
For example, one stick can represent one cow. If each cow has one stick, the sticks help check whether all cows returned.
Q5. Why are sticks or tally marks not convenient for large numbers?
Sticks and tally marks need one mark for each object.
For a large number, this becomes slow and difficult. That is why people developed grouped symbols and later place value systems.
Number System Class 8 Maths Important Questions
Number system class 8 maths questions become easier when students understand why counting methods changed. Number systems became better when people learned to group objects and write large numbers clearly.
Class 8 Maths Chapter 3 Question Answer on Number Systems
Q1. What is the role of a fixed order in a number system?
A fixed order helps people count correctly.
When every object gets matched to the next object, sound or symbol in the sequence, the last match tells the size of the collection.
Q2. What are landmark numbers?
Landmark numbers are reference numbers used to represent other numbers.
For example, in the Roman system, I, V, X, L, C, D and M represent 1, 5, 10, 50, 100, 500 and 1000. These help write larger numbers.
Q3. Why is grouping useful in number systems?
Grouping reduces the number of symbols needed.
Instead of writing many individual marks, people can group numbers by 2, 5, 10, 20 or another fixed size. This makes representation shorter.
Q4. What is a base-n number system?
A base-n number system has landmark numbers that are powers of (n).
The landmark numbers are:
1, n, n^2, n^3, ...
For example, the Egyptian number system is a base-10 system.
Q5. What is a decimal number system?
A decimal number system is a base-10 number system.
Its landmark numbers are powers of 10:
1, 10, 100, 1000, ...
The Hindu number system is a decimal place value system.
A Story of Numbers Class 8 Questions on Early Counting
A Story of Numbers Class 8 shows that counting began before modern digits. Early counting methods were useful, but each had a limitation.
Q1. How did people count before written numerals?
People counted using fingers, body parts, pebbles, sticks, knots, tally marks, sounds and marks on bones or walls.
These methods helped them compare and remember quantities.
Q2. How does one-to-one mapping help in counting animals?
One stick can be matched with one animal.
If a shepherd has one stick for each sheep, the sticks can help check whether every sheep returned. This avoids recounting from memory.
Q3. Why did tally marks become difficult for large numbers?
Tally marks need one mark for each object.
For 500 objects, a person needs 500 marks. This is slow, crowded and easy to misread.
Q4. Why did humans create symbols for numbers?
Humans created symbols to record numbers faster and more clearly.
Symbols made it easier to count trade goods, land, taxes, offerings, time and stored food.
Q5. Why is number history important for students?
Number history helps students understand that mathematics developed to solve real problems.
It also shows why place value and zero were major breakthroughs.
Roman Numerals Class 8 Important Questions
Roman numerals class 8 questions show how landmark symbols can represent numbers. This system is useful for writing some numbers, but it is not very efficient for calculations.
Q1. What are the main Roman numerals?
The main Roman numerals are:
I, V, X, L, C, D, M
They represent:
1, 5, 10, 50, 100, 500, 1000
Q2. Write 27 in Roman numerals.
Break 27 into landmark numbers.
27 = 10 + 10 + 5 + 1 + 1
So:
27 = XXVII
Q3. Write 2367 in Roman numerals.
Break 2367 into landmark numbers.
2367 = 1000+1000+100+100+100+50+10+5+1+1
So:
2367 = MMCCCLXVII
Q4. Write 715 in Roman numerals.
715 = 500 + 100 + 100 + 10 + 5
So:
715 = DCCXV
Q5. Why is the Roman number system less efficient for arithmetic?
The Roman system does not use a regular base and place value.
This makes addition possible but lengthy. Multiplication and division become much harder without a calculating device like an abacus.
Egyptian Number System Class 8 Questions
The Egyptian number system class 8 section is important because it shows the idea of base 10 through landmark numbers.
Q1. What is special about the Egyptian number system?
The Egyptian number system uses powers of 10 as landmark numbers.
Its landmark numbers include:
1, 10, 100, 1000, ...
Each landmark number is 10 times the previous one.
Q2. Why is the Egyptian number system called a base-10 system?
It is called base-10 because each landmark number is obtained by multiplying the previous one by 10.
For example:
1, 10, 100, 1000
These are powers of 10.
Q3. Represent 324 using the Egyptian system idea.
Break 324 into powers of 10.
324 = 100 + 100 + 100 + 10 + 10 + 1 + 1 + 1 + 1
So, it needs three 100-symbols, two 10-symbols and four 1-symbols.
Q4. What is the drawback of the Egyptian system?
The Egyptian system needs a new symbol for every higher power of 10.
For very large numbers, this becomes difficult because the system needs more and more new symbols.
Q5. Why were calculations easier in the Egyptian system than in Roman numerals?
The Egyptian system uses powers of 10 as landmark numbers.
Products of landmark numbers lead to other landmark numbers. This makes arithmetic more regular than in the Roman system.
Base-n Number System Class 8 Important Questions
Base-n number system class 8 questions help students understand why powers matter in number representation. A base system groups numbers using powers of one chosen number.
Q1. What are the landmark numbers in a base-5 system?
In base 5, the landmark numbers are powers of 5.
5^0=1
5^1=5
5^2=25
5^3=125
5^4=625
Q2. Express 143 using base-5 landmark numbers.
Use the largest power of 5 less than 143.
143 = 125 + 5 + 5 + 5 + 1 + 1 + 1
So, 143 has one 125, three 5s and three 1s in this base-5 grouping.
Q3. Write the landmark numbers of a base-7 system.
The landmark numbers are powers of 7.
7^0=1
7^1=7
7^2=49
7^3=343
7^4=2401
Q4. Can every whole number be represented in a base-n system?
Yes, every whole number can be represented in a base-n system.
The number is grouped using powers of (n). Then each group count is written according to the system’s symbols.
Q5. Why are base systems useful for multiplication?
Base systems use landmark numbers that are powers of one number.
When two landmark numbers multiply, the result is another landmark number. This makes multiplication easier and more systematic.
Place Value System Class 8 Maths Questions
Place value system class 8 maths questions are central to this chapter. Place value solved a major problem because the same symbol could show different values in different positions.
Q1. What is a place value system?
A place value system is a number system where a symbol’s value depends on its position.
For example, in 375:
3 × 100 + 7 × 10 + 5 × 1
The digit 3 means 300 because it is in the hundreds place.
Q2. Why was place value an important breakthrough?
Place value allowed people to write very large numbers using a small set of symbols.
Instead of creating new symbols for every large landmark number, positions showed whether a digit meant ones, tens, hundreds or more.
Q3. What problem did blank spaces create in old place value systems?
Blank spaces made numbers confusing.
In the Mesopotamian system, a blank could mean no value in a place, but spacing was not always clear. This caused ambiguity while reading numbers.
Q4. How did zero solve the place value problem?
Zero worked as a placeholder.
It clearly showed that a place had no value. For example, in 305, zero shows that there are no tens.
Q5. Why is zero more than a placeholder in the Hindu number system?
In the Hindu number system, zero is also treated as a number.
It can be used in arithmetic. For example, adding 0 to a number gives the same number, and multiplying by 0 gives 0.
Hindu Number System Class 8 Important Questions
The Hindu number system class 8 section is the most important part of the chapter. The modern system became powerful because it combined base 10, place value and zero.
Q1. What is the Hindu number system?
The Hindu number system is a base-10 place value system that uses ten digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
It represents numbers clearly using place value.
Q2. Why is the Hindu number system efficient?
It uses only ten symbols to represent all numbers.
Place value shows the value of each digit. Zero removes ambiguity. This makes writing and calculation simple.
Q3. How did the Hindu number system spread across the world?
The system developed in India and later reached the Arab world.
From there, it travelled to Europe and other regions. Over time, it became the global number system because it made computation efficient.
Q4. Why are Hindu numerals sometimes called Hindu-Arabic numerals?
They are called Hindu-Arabic numerals because the system originated in India and reached Europe through the Arab world.
Arab scholars called them Hindu numerals. European scholars later learned them through Arabic works.
Q5. Why is zero considered a major invention?
Zero made place value unambiguous and also became a number.
It allowed efficient arithmetic, scientific calculation, accounting, computing and modern mathematics.
Class 8 Maths Chapter 3 Extra Questions with Answers
Class 8 maths chapter 3 extra questions help students practise conversions, reasoning and comparison between number systems.
Q1. Represent 1222 in Roman numerals.
1222 = 1000 + 100 + 100 + 10 + 10 + 1 + 1
So:
1222 = MCCXXII
Q2. Represent 2999 in Roman numerals using the chapter’s additive style.
2999 = 1000+1000+500+100+100+100+100+50+10+10+10+5+1+1+1+1
So:
2999 = MMDCCCCLXXXXVIIII
Some modern Roman numeral rules write this differently. The chapter’s approach shows grouping by landmark numbers.
Q3. Represent 302 in Roman numerals.
302 = 100 + 100 + 100 + 1 + 1
So:
302 = CCCII
Q4. Write 15, 50 and 137 using base-5 grouping.
Base-5 landmark numbers are:
1, 5, 25, 125
For 15:
15 = 5 + 5 + 5
For 50:
50 = 25 + 25
For 137:
137 = 125 + 5 + 5 + 1 + 1
Q5. Write 25 in base 8, base 5 and base 2.
Base 8:
25 = 3 × 8 + 1
So:
25 = 31_8
Base 5:
25 = 1 × 25 + 0 × 5 + 0
So:
25 = 100_5
Base 2:
25 = 16 + 8 + 1
So:
25 = 11001_2
Comparing Number Systems Class 8 Questions
These questions help students understand why some systems were replaced by more efficient ones. A good answer should compare symbols, base, place value and zero.
Q1. How is the Roman system different from the Hindu number system?
The Roman system uses landmark symbols such as I, V, X, L, C, D and M.
The Hindu number system uses digits 0 to 9 with place value. This makes large numbers and calculations much easier.
Q2. How is the Egyptian system different from the Hindu number system?
The Egyptian system uses separate symbols for powers of 10.
The Hindu system uses place value. It does not need a new symbol for every higher power of 10.
Q3. Why is place value better than repeated symbols?
Repeated symbols become long and difficult for large numbers.
Place value makes writing compact. For example, 5000 can be written with one digit and place instead of many repeated marks.
Q4. Why did zero make number writing clearer?
Zero shows that a place is empty.
For example, 105 and 15 are different because zero marks the tens place in 105. Without zero, the number could become confusing.
Q5. Which number system is most efficient for modern calculation?
The Hindu number system is most efficient for modern calculation.
It uses ten digits, base 10, place value and zero. This makes arithmetic compact and systematic.
Class 8 Maths Chapter 3 MCQs with Answers
Class 8 Maths Chapter 3 MCQs test definitions, Roman numerals, base systems, place value and zero. These are useful for quick revision before long answers.
Q1. A number system needs a standard sequence with:
(a) No order
(b) Fixed order
(c) Only pictures
(d) Only Roman symbols
Answer: (b) Fixed order
Counting needs a fixed sequence of objects, names or symbols.
Q2. The symbols used to represent numbers are called:
(a) Variables
(b) Numerals
(c) Fractions
(d) Landmarks
Answer: (b) Numerals
Numerals are written symbols for numbers.
Q3. The Roman numeral X represents:
(a) 5
(b) 10
(c) 50
(d) 100
Answer: (b) 10
X is the Roman numeral for 10.
Q4. A base-10 system has landmark numbers:
(a) Powers of 2
(b) Powers of 5
(c) Powers of 10
(d) Powers of 60
Answer: (c) Powers of 10
Base 10 uses (1, 10, 100, 1000, ...).
Q5. The Mesopotamian system was mainly based on:
(a) Base 2
(b) Base 5
(c) Base 10
(d) Base 60
Answer: (d) Base 60
It used the sexagesimal system.
Q6. Zero helps in a place value system because it:
(a) Removes all digits
(b) Works as a placeholder
(c) Makes numbers smaller only
(d) Replaces multiplication
Answer: (b) Works as a placeholder
Zero shows that a place has no value.
Competency-Based Questions on A Story of Numbers Class 8
Competency-based questions test whether students can explain the reason behind number systems. Students should not only name the system.
Q1. A shepherd uses stones to count goats. Which counting idea is being used?
The shepherd is using one-to-one mapping.
Each stone represents one goat. If every goat has one matching stone, the shepherd can check the total without using written numerals.
Q2. A number system has symbols for 1, 10, 100 and 1000. Which idea does it show?
It shows the idea of landmark numbers.
If each landmark is 10 times the previous one, the system is based on powers of 10.
Q3. Why would 305 be difficult to write clearly without zero?
Without zero, the tens place may look empty or unclear.
Zero shows that there are no tens in 305. It separates 305 from 35 or 3005.
Q4. Why is a place value system better for very large numbers?
A place value system uses position to show value.
This means the same digits can represent very large numbers without creating new symbols for every larger quantity.
Q5. Why should students learn old number systems?
Old number systems show how mathematical ideas developed.
They help students understand why place value and zero made modern arithmetic faster and clearer.
Class 8 Maths Important Questions Chapter-Wise