Class 8 Maths · Original EZT practice
A Story of Numbers (Class 8 Maths Chapter 3): how humans learned to write numbers
Numbers feel obvious today, but writing them took thousands of years. This chapter travels from tally marks scratched on bones to Roman numerals to the Hindu-Arabic system with zero - the one that made fast arithmetic possible. Below: the story in plain words, then original EZT practice with worked answers. (Note: this is original practice, not a textbook exercise key.)
10 original worked examples, 10 fresh self-check questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 17 October 2026:
1. Before numerals: counting with marks and objects
Early counting used one mark or object per thing counted - tally sticks, knots and pebbles. It works for small counts but becomes hard to read once numbers grow.
2. Roman numerals: a letter system
Roman numerals use letters: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000. Add when a smaller letter follows a bigger one, and subtract when it comes before.
3. Why the Roman system ran out of road
Roman numerals have no zero and no place value. Each letter keeps the same value wherever it sits, so written arithmetic is slow and large numbers need long strings.
4. The Hindu-Arabic leap: place value and zero
In the Hindu-Arabic system a digit value depends on its position. Zero is both a number and a placeholder, which lets 406 and 46 mean different things. This system grew in India and travelled through the Arab world to Europe.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Write a count in tally marks
Choose the method: Group five marks first, then count the remaining single marks.
EZT practice question
Write 17 in tally marks using groups of five.
Show the worked solution
- Three full groups make 15.
- Two single marks remain.
Answer: Three groups of five plus two single marks.
Check: 5 + 5 + 5 + 2 = 17.
Watch for this: Do not draw seventeen separate marks when the task asks for groups of five.
Now try it yourself
Write 23 in tally groups of five.
Check your answer
Four groups of five plus three single marks.
4 × 5 + 3 = 23.
Explain why grouping helps
Choose the method: Compare counting every mark with counting complete groups first.
EZT practice question
Why did grouping tally marks in fives or tens help early counters?
Show the worked solution
- A large number becomes several smaller groups.
- The reader can count groups instead of every mark.
Answer: Grouping makes a large count faster to read and check.
Check: Ten groups of five are quicker to count than fifty separate marks.
Watch for this: Grouping does not change the total; it changes how the total is organised.
Now try it yourself
How many groups of five are in 45?
Check your answer
Nine groups.
45 / 5 = 9.
Build a Roman numeral
Choose the method: Break the number into tens, fives and ones, then write the letters from largest to smallest.
EZT practice question
Write 27 in Roman numerals.
Show the worked solution
- 27 = 10 + 10 + 5 + 2.
- 10 + 10 + 5 + 2 becomes X + X + V + II.
Answer: XXVII.
Check: XXVII reads as 10 + 10 + 5 + 1 + 1 = 27.
Watch for this: Do not write five as five separate I letters.
Now try it yourself
Write 38 in Roman numerals.
Check your answer
XXXVIII.
38 = 10 + 10 + 10 + 5 + 3.
Read a subtractive Roman numeral
Choose the method: When a smaller letter comes before a larger one, subtract the smaller value.
EZT practice question
What number is XIV?
Show the worked solution
- X is 10.
- IV is 5 - 1 = 4.
Answer: 14.
Check: 10 + 4 = 14.
Watch for this: Do not read IV as 6; the smaller I comes before V.
Now try it yourself
What number is XIX?
Check your answer
19.
X + IX = 10 + 9 = 19.
Read XL in a numeral
Choose the method: Read XL as 50 - 10 before adding the letters that follow.
EZT practice question
What number is XLII?
Show the worked solution
- XL is 50 - 10 = 40.
- II is 2.
Answer: 42.
Check: 40 + 2 = 42.
Watch for this: Do not read X and L separately as 60; order matters.
Now try it yourself
What number is XCIV?
Check your answer
94.
XC + IV = 90 + 4 = 94.
Write a large Roman numeral
Choose the method: Split into hundreds, tens and ones, using subtraction for 900, 90 and 9.
EZT practice question
Write 999 in Roman numerals.
Show the worked solution
- 999 = 900 + 90 + 9.
- 900 is CM, 90 is XC and 9 is IX.
Answer: CMXCIX.
Check: CM + XC + IX = 900 + 90 + 9 = 999.
Watch for this: Do not write nine separate C letters for 900.
Now try it yourself
Write 444 in Roman numerals.
Check your answer
CDXLIV.
444 = 400 + 40 + 4 = CD + XL + IV.
Write a year in Roman numerals
Choose the method: Write the thousands first, then the remaining tens and ones.
EZT practice question
Write 2026 in Roman numerals.
Show the worked solution
- 2026 = 2000 + 20 + 6.
- 2000 is MM, 20 is XX and 6 is VI.
Answer: MMXXVI.
Check: MM + XX + VI = 2000 + 20 + 6 = 2026.
Watch for this: There is no single Roman letter for 2000; repeat M twice.
Now try it yourself
Write 2030 in Roman numerals.
Check your answer
MMXXX.
2030 = 2000 + 30.
See why place value matters
Choose the method: Try to imagine column multiplication when every letter has one fixed value.
EZT practice question
Why is multiplying CCCXII by XXIV awkward using only Roman ideas?
Show the worked solution
- There is no zero to hold an empty place.
- Each letter keeps the same value, so there is no column method.
Answer: The letters must be expanded and regrouped by hand, without place value or zero.
Check: Hindu-Arabic columns use position to multiply by ones, tens and hundreds.
Watch for this: The symbols are not the problem alone; the missing place-value structure is.
Now try it yourself
Which feature makes 406 different from 46?
Check your answer
Zero as a placeholder.
The zero keeps the 4 in the hundreds place.
Read place value for one digit
Choose the method: Name the place where the digit sits before giving its value.
EZT practice question
What does the digit 7 stand for in 7452 and in 2745?
Show the worked solution
- In 7452, 7 is in the thousands place.
- In 2745, 7 is in the hundreds place.
Answer: 7000 in 7452 and 700 in 2745.
Check: 7452 starts with 7 thousands; 2745 has 7 hundreds.
Watch for this: The digit alone does not fix its value; position does.
Now try it yourself
What does 6 stand for in 60606?
Check your answer
60000, 600 and 6.
The three 6 digits sit in the ten-thousands, hundreds and ones places.
Explain zero as a placeholder
Choose the method: Remove the zero and check whether the other digits keep their places.
EZT practice question
Why is zero called a placeholder in 5082?
Show the worked solution
- The zero holds the hundreds place.
- Without it, the digits would read as 582.
Answer: It keeps 5 in the thousands place and 8 in the tens place.
Check: 5082 = 5000 + 80 + 2, while 582 = 500 + 80 + 2.
Watch for this: Zero is not merely nothing here; it preserves place value.
Now try it yourself
Which digit is the placeholder in 7305?
Check your answer
The zero.
It holds the tens place.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Write 58 in Roman numerals.
- What number is XCIV?
- Write your birth year in Roman numerals.
- In 60606, what does each 6 stand for?
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Questions about this practice page
- What are tally marks?
- One mark per item counted, grouped in fives for quick reading - an early written counting method used before numerals.
- How do Roman numerals work?
- Letters stand for values. A smaller letter after a bigger one adds, and before it subtracts - so IV is 4 and VI is 6.
- Why is the Hindu-Arabic system better for arithmetic?
- Place value lets ten digits write any number, and zero holds empty places so column addition and multiplication work.
- Who invented zero?
- Zero as a number with a symbol developed in India. Brahmagupta wrote rules for calculating with it in the 7th century, and it later spread through Arab mathematics to Europe.
- Are these the NCERT exercise questions for A Story of Numbers?
- No. EZT pages are original practice on this chapter - use them to prepare for the textbook exercises, not as a substitute for your book.