A Story of Numbers Class 8 Maths Worksheet with Answers Chapter 3

Ganita Prakash Part-I, Grade 8, Textbook of Mathematics – Here we are with another chapter of Maths for class 8. Chapter 3, “A Story of Numbers,” is not very tough, as you don’t need many concepts. Let’s try to do this worksheet quickly after you have done with the chapter fully. Again, the worksheet is divided into 4 parts – Basic, Standard, Advance, and HOTS. Answers are there at the bottom.

Class 8 Maths Worksheet – Chapter 3: A Story of Numbers

Basic

1. Match the Roman symbols with their values: I, V, X, L, C, D, M.
2. Write in Roman numerals: 14, 27, 39.
3. Write in Hindu-Arabic (our number system): XLII, LXXXVII, CIX.
4. Fill in the blanks:
   (a) A base-10 number system is called a __________ number system.
   (b) In a base-n system, the landmark numbers are __________ of n (starting from n⁰).
5. Expand using place value: 5074 = ______ × 10³ + ______ × 10² + ______ × 10 + ______ × 1
6. Write the number shown by this expansion:
   2 × 10³ + 6 × 10² + 3 × 10 + 4 × 1 = ______

Standard

1. Write in Roman numerals: 1222, 302.
2. Convert the Roman numeral to Hindu-Arabic: MMCCCLXII.
3. Base-5 conversion (digits form):
   Write 143 in base-5 using place values (no special symbols needed). (Answer like 1033₅)
4. Write the first five landmark numbers of base-7: (from 7⁰ onwards)
5. True/False (give one-line reason): Every whole number can be represented in base-5.
6. Expanded form using powers of 10:
   375 = ______ × 10² + ______ × 10 + ______ × 1

Advance

1. Add (you may convert to Hindu-Arabic to verify):
   CCXXXII + CCCCXIII = ______ (Write the final answer in Roman numerals.)
2. Multiply (write answers in Hindu-Arabic):
   (a) V × L = ______
   (b) V × D = ______
   (c) L × D = ______
3. Convert to base-5 (digits form): 651 = ______₅
4. Concept question: Explain in one or two lines why “0” is important in a place value system. Use the pair 507 and 57 as an example.
5. Create-your-own base-4:
   Suppose digits are A=0, B=1, C=2, D=3. Write 23 (decimal) in this system.
6. Landmark numbers: Write the first four landmark numbers of base-12 (from 12⁰ onwards).

HOTS

1. Thinking question: Roman numerals have landmark numbers (1, 5, 10, 50, …). Still, why is multiplication considered difficult in the Roman system? (2–3 lines)
2. Reasoning: Is there any whole number that cannot be represented in base-7? Explain.
3. Base-6 challenge: What is the largest 3-digit number in base-6? Also write its value in decimal.
4. Trick check (validity):
   Can “2634” be a valid numeral in base-5 if we keep the digits the same? Explain why/why not.
5. Roman pattern spotting:
   Find one number between 1 and 100 whose Roman numeral uses only one type of symbol (repetition allowed). Write the number and its Roman numeral.
6. Carry logic: In base-n addition, why do we “carry” when a digit-sum reaches n? Explain in a simple example (choose any base you like).

Answer Key (with short hints)

Basic – Answers

1. I=1, V=5, X=10, L=50, C=100, D=500, M=1000
2. 14 = XIV, 27 = XXVII, 39 = XXXIX
3. XLII = 42, LXXXVII = 87, CIX = 109
4. (a) decimal (b) powers (Hint: n⁰, n¹, n², …)
5. 5074 = 5 × 10³ + 0 × 10² + 7 × 10 + 4 × 1
6. 2634 (Hint: just add the place values)

Standard – Answers

1. 1222 = MCCXXII, 302 = CCCII
2. MMCCCLXII = 2367 (Hint: 2000+300+60+7)
3. 143 = 1×125 + 0×25 + 3×5 + 3×1 → 1033₅
4. 7⁰=1, 7¹=7, 7²=49, 7³=343, 7⁴=2401
5. True (Hint: base systems represent all whole numbers using place values)
6. 375 = 3×10² + 7×10 + 5×1

Advance – Answers

1. CCXXXII = 232, CCCCXIII = 413, sum = 645 = DCXLV
2. (a) 250 (b) 2500 (c) 25000 (Hint: convert V=5, L=50, D=500)
3. 651 = 10101₅ (Hint: 1×625 + 1×25 + 1×1)
4. 0 keeps the place value correct: 507 has “0 tens”, but 57 has “5 tens”. Without 0, positions collapse.
5. 23 decimal = 113₄ → using symbols: B B D (since 1,1,3) → BBD
6. 12⁰=1, 12¹=12, 12²=144, 12³=1728

HOTS – Answers

1. Because regrouping is not uniform: sometimes 5 of one symbol makes the next (like 5 C = D), and subtraction rules (IV, IX) add extra rules. So algorithms are messy.
2. No. Every whole number can be represented in base-7 using digits 0–6 and place values.
3. Largest 3-digit base-6 number is 555₆. Decimal value = 5×6² + 5×6 + 5 = 5×36 + 30 + 5 = 215.
4. No. In base-5, allowed digits are only 0–4. The digit 6 is invalid, so “2634” cannot be a base-5 numeral.
5. Example: 30 = XXX (only X used). (Many answers possible: 20=XX, 3=III, 50=L, etc.)
6. Because n of a lower place equals 1 of the next place. Example (base-5): 4 + 3 = 7 → write 2, carry 1 because 7 = 1×5 + 2.

Worksheet From Other Chapters

Ganita Prakash Part-I

• A Square and a Cube Class 8 Maths Worksheet with Answers
• Power Play Class 8 Maths Worksheet with Answers
• Number Play Class 8 Maths Worksheet with Answers
• We Distribute, Yet Things Multiply Class 8 Maths Worksheet with Answers
• Proportional Reasoning-1 Class 8 Maths Worksheet with Answers

Ganita Prakash Part-II

• Fractions in Disguise Class 8 Maths Worksheet with Answers
• Proportional Reasoning–2 Class 8 Maths Worksheet with Answers
• Algebra Play Class 8 Maths Worksheet with Answers