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A Story of Numbers – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 3. Notes, key terms, important questions with answers and MCQs.

Chapter overview

People counted long before writing numbers. Over time many number systems were used, and the Indian place-value system with zero became the one used worldwide.

Early number systems

Tally marks and grouping (fives, tens) were the first records of counting.
Egyptian and Roman numerals used symbols that are added (Roman: I, V, X, L, C, D, M).
Roman numerals have no zero and no place value, so calculation is hard.

Place value and zero

In the Hindu–Arabic system the value of a digit depends on its place (ones, tens, hundreds…).
Zero as a number and as a placeholder developed in India (Brahmagupta gave rules for zero).
Other bases exist: base 2 (binary) in computers, base 60 in time (60 seconds, 60 minutes).

Key terms

Place value: value of a digit from its position
Base: number of digits used in a system (10 in decimal)
Roman numerals: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000

Formulas

4 = IV, 9 = IX, 40 = XL, 90 = XC

Important questions with answers

What is the role of zero in the Indian place-value system?2 marks

Zero holds an empty place, so 205 and 25 can be told apart; it made writing and calculating large numbers easy.

Write 2,024 in Roman numerals and 25 in base 2.3 marks

2,024 = MMXXIV. 25 = 16 + 8 + 1 = 11001₂.

Compare the Roman numeral system with the Hindu–Arabic place-value system. Why did the place-value system spread across the world?5 marks

Roman numerals use letters (I, V, X, L, C, D, M) whose values are added or subtracted; there is no zero and no place value, so large numbers are long and arithmetic is hard. The Hindu–Arabic system uses ten digits including 0, and the value of a digit depends on its place (ones, tens, hundreds…). Any number can be written with just ten symbols, and addition, multiplication and division follow simple column methods, which is why it spread worldwide through trade and scholars.

Quick revision

Zero and place value came from India.
Decimal system is base 10.
Time uses base 60.

Exam tips

In Roman numerals, a smaller symbol before a bigger one is subtracted.
In binary, 1011₂ = 8 + 0 + 2 + 1 = 11.

Practice MCQs

XIV in our numerals is
1. 14
2. 16
3. 9
4. 11
Show answer
Answer: (a) 14. 10 + 4.
The system we use daily is base
1. 2
2. 8
3. 10
4. 60
Show answer
Answer: (c) 10. Decimal.
The place value of 7 in 47,315 is
1. 7
2. 700
3. 7000
4. 70,000
Show answer
Answer: (c) 7000. Thousands place.
Which Roman numeral equals 90?
1. XC
2. LXL
3. LXXXX
4. IC
Show answer
Answer: (a) XC. 100 − 10.
The Roman numeral for 49 is
1. XLIX
2. IL
3. XXXXIX
4. LIX
Show answer
Answer: (a) XLIX. XL (40) + IX (9).
The binary number 1101 equals
1. 11
2. 12
3. 13
4. 14
Show answer
Answer: (c) 13. 8 + 4 + 0 + 1.
Why was calculation hard with Roman numerals?
1. they had no place value and no zero
2. they used too many symbols only
3. they used base 2
4. they were written right to left
Show answer
Answer: (a) they had no place value and no zero. No positional system.
The binary number 1011 equals
1. 13
2. 11
3. 9
4. 1011
Show answer
Answer: (b) 11. 8 + 0 + 2 + 1.

All chapters of Class 8 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.