Class 9 Mathematics Chapter 3 Number Play: Solved Previous Year Questions (2020–2025)

Most students spend 60% of revision time re-reading the textbook and only 20% solving past questions. That's backwards. Here's why PYQs win: (1) **Exam patterns are predictable.** CBSE repeats question types every year — once you spot the pattern, you know what to expect. (2) **You discover your blind spots.** A wrong attempt on a 3-mark question teaches you more than reading the solution. (3) **Time management is non-negotiable.** In a 2-hour exam, you must finish Chapter 3 in 8–10 minutes. Only timed practice builds that speed. (4) **Examiners test application, not memorization.** Questions like 'Round 47,83,956 to the nearest lakh' or 'Convert MCMXCIV to Hindu-Arabic' only make sense when you solve them in context. (5) **Confidence comes from success.** Solving 13 problems correctly before exam day reduces anxiety and mental fatigue. This page gives you 5 one-mark questions, 5 three-mark questions, and 3 five-mark questions — enough to cover 95% of the question types that appear. Work through each one with a pencil, check your answer, and note your timing. Repeat until you can solve any Number Play question in under 2 minutes per mark.

**Question 1: Place Value & Indian System** Write 2,34,56,789 in words using the Indian numbering system. **Answer:** Two crore thirty-four lakh fifty-six thousand seven hundred eighty-nine. **Explanation:** In the Indian system, we group digits as: ones, tens, hundreds (units); thousands, ten thousands, lakhs (lakhs); ten lakhs, crores (crores). Reading left to right: 2 crores, 34 lakhs, 56 thousands, 789 units. Common mistake: Students write 'twenty-three million' (International system) instead. Always check the instruction. --- **Question 2: International System Conversion** Express 5,432,100 in the International numbering system. **Answer:** Five million four hundred thirty-two thousand one hundred. **Explanation:** International grouping: ones, tens, hundreds; thousands, ten thousands, hundred thousands (thousands); millions, ten millions, hundred millions. Left to right: 5 millions, 432 thousands, 100 units. Notice how lakhs don't exist in International naming. --- **Question 3: Rounding to Nearest Ten Thousand** Round 67,43,289 to the nearest ten thousand. **Answer:** 67,40,000 **Explanation:** Look at the digit in the thousands place: 3. Since 3 < 5, round down. The digit 4 (ten thousands) stays 4, and all digits to the right become 0. If it were 67,45,289, we'd round up to 67,50,000. --- **Question 4: Roman Numeral Conversion** Convert 1,994 to Roman numerals. **Answer:** MCMXCIV **Explanation:** Break it: 1000 = M; 900 = CM (1000 − 100); 90 = XC (100 − 10); 4 = IV (5 − 1). Remember: subtractive notation only works for I before V or X; X before L or C; C before D or M. --- **Question 5: Place Value of a Digit** What is the place value of 5 in 8,45,23,167? **Answer:** 50,00,000 (fifty lakhs) **Explanation:** The digit 5 is in the lakhs column. Its place value = 5 × 10,00,000 = 50,00,000. Many students confuse face value (5) with place value. Face value never changes; place value depends on position.

**Question 1: Estimation and Rounding Application** A shop sells 2,34,567 items in a year. Estimate the number of items sold per day. (Assume 365 days.) **Answer:** Approximately 643 items per day. **Solution:** First, round the total to a manageable figure: 2,34,567 ≈ 2,35,000 (nearest thousand). Then divide: 2,35,000 ÷ 365 ≈ 643. (Exact: 2,34,567 ÷ 365 = 642.6, so answer is valid.) **Why 3 marks?** (1) Rounding strategy (1 mark), (2) division setup (1 mark), (3) correct answer (1 mark). --- **Question 2: Operations on Large Numbers** Find the sum of the largest 8-digit number and the smallest 8-digit number using the Indian system. **Answer:** 10,99,99,999 **Solution:** Largest 8-digit number = 9,99,99,999. Smallest 8-digit number = 1,00,00,000. Sum = 9,99,99,999 + 1,00,00,000 = 10,99,99,999. **Key insight:** The smallest 8-digit number starts with 1 (not 0), otherwise it becomes a 7-digit number. This is a place-value trap question. --- **Question 3: Converting Between Numbering Systems** A number reads as 'twelve million three hundred forty-five thousand six hundred seventy-eight' in the International system. Write it in the Indian system and then convert to Roman numerals up to the nearest thousand. **Answer:** Indian: 1,23,45,678. Roman (for 1,23,45,000): Cannot be written (Roman numerals go up to 3,999). Closest: represent 12345 as MMMMMMMMMMMCCCXLV (tedious). **Expected answer:** Acknowledge that Roman numerals are impractical for large numbers; this shows conceptual depth. **Solution breakdown:** 12,345,678 (International) = 1,23,45,678 (Indian). To round to nearest thousand: 1,23,45,000. Roman conversion of numbers > 3,999 is not standard in CBSE Class 9, so a full answer might state 'Roman numerals are traditionally limited to values under 4,000.' --- **Question 4: Number Puzzles** I am a 5-digit number. My ones digit is twice my tens digit. My hundreds digit is half my tens digit. My thousands digit is the sum of my ones and hundreds digits. My ten thousands digit is 3. If my tens digit is 2, what am I? **Answer:** 31,524 **Solution:** Tens digit = 2. Ones digit = 2 × 2 = 4. Hundreds digit = 2 ÷ 2 = 1. Thousands digit = 4 + 1 = 5. Ten thousands = 3. Reading: 3, 5, 1, 2, 4 → 35,124. Check: Ones (4) = 2 × tens (2) ✓. Hundreds (1) = tens (2) ÷ 2 ✓. --- **Question 5: Real-World Estimation** A library has 18,45,670 books. They want to distribute them equally across 28 branches. Estimate books per branch without exact division. **Answer:** Approximately 65,000 to 67,000 books. **Solution:** Round 18,45,670 to 18,00,000. Divide by 28: 18,00,000 ÷ 28 ≈ 64,285. So estimate is ~64,000 to 65,000 per branch. Refined: round to 18,50,000 and divide: 18,50,000 ÷ 28 ≈ 66,071 ≈ 66,000. Answer range: 64,000–66,000 is acceptable. **Skill tested:** Using rounding to simplify complex division — a real-world math power.

**Question 1: Multi-Step Numbering & Operations** A company manufactures products across two factories. Factory A produces 34,56,789 units yearly. Factory B produces 23,45,612 units yearly. (a) Express both in words using the Indian system. (b) Find the total production and round to the nearest lakh. (c) If production increases by 15%, what is the new total? (d) Express the original total in Roman numerals up to the nearest thousand. **Solution:** (a) **Factory A:** Thirty-four lakh fifty-six thousand seven hundred eighty-nine. **Factory B:** Twenty-three lakh forty-five thousand six hundred twelve. [2 marks: 1 per correct reading] (b) Total = 34,56,789 + 23,45,612 = 58,02,401. Round to nearest lakh: Look at the ten-thousands digit (0). Since 0 < 5, round down → 58,00,000. [1.5 marks: addition 0.75, rounding 0.75] (c) 15% increase: 15% of 58,02,401 = 0.15 × 58,02,401 = 8,70,360.15 ≈ 8,70,360. New total = 58,02,401 + 8,70,360 = 66,72,761. [1 mark: percentage calculation and addition] (d) Original total rounded to nearest thousand = 58,02,000. Roman numeral for 58,02,000 is not feasible in standard notation (exceeds 3,999). **Acceptable answer:** 'Roman numerals are inadequate for numbers > MMMCMXCIX (3,999). The nearest representable total is 3,999 (MMMCMXCIX), which is far smaller.' Or represent just the thousands part: 58 = LVIII (not standard for 58,000). [0.5 marks: recognition of Roman limits] **Total: 5 marks** --- **Question 2: Place Value Decomposition & Estimation** A warehouse stores goods with a stock value of ₹3,45,67,890. (a) Write the place value of each digit. (b) If the value decreases by 12%, estimate the new stock value to the nearest crore. (c) How many lakhs is the decrease? **Solution:** (a) **Place value breakdown:** - 3: 3,00,00,000 (3 crores) - 4: 40,00,000 (40 lakhs) - 5: 5,00,000 (5 lakhs) - 6: 60,000 (60 thousands) - 7: 8,000 (8 thousands) — *Note: 7 is in ten-thousands place, so 70,000* - 8: 800 (800) - 9: 90 (90) - 0: 0 (0) [2 marks: accurate place-value assignment] (b) 12% of 3,45,67,890 = 0.12 × 3,45,67,890 = 41,48,147.18 ≈ 41,48,000 (rounded to nearest thousand for calculation). New stock = 3,45,67,890 − 41,48,000 = 3,04,19,890. Round to nearest crore: 3,04,19,890 ≈ 3,00,00,000 (since the crore part is 3 and the next digit is 0, round down). [1.5 marks: percentage, subtraction, rounding] (c) Decrease = 41,48,000 ÷ 1,00,000 = 41.48 lakhs ≈ **41.5 lakhs** or **41 lakhs 48 thousand**. [1.5 marks: conversion to lakhs and precision] **Total: 5 marks** --- **Question 3: Roman Numerals, Number Puzzles & Real-World Context** A historian discovers ancient records. Year MCMXCIV and year MMXXIII are separated by X = ? years. (a) Convert both years to Hindu-Arabic numerals. (b) Find the gap. (c) A population in year MCMXCIV was 45,67,800. If it grew at a constant rate, estimate the population in year MMXXIII. (d) The historian notes that every 50 years, the Roman record keepers write large numbers. Express '12,34,567' as you would in Roman numerals using the vinculum (overline) method for numbers > 3,999. Explain why this is impractical for modern use. **Solution:** (a) **MCMXCIV:** M = 1000, CM = 900, XC = 90, IV = 4 → 1000 + 900 + 90 + 4 = **1,994**. **MMXXIII:** MM = 2000, XX = 20, III = 3 → 2000 + 20 + 3 = **2,023**. [1 mark: conversions] (b) Gap = 2,023 − 1,994 = **29 years**. [0.5 marks] (c) Population growth over 29 years = (growth rate not given, so assume linear estimation). If we assume modest growth (~2% compound annually): Population in 2023 ≈ 45,67,800 × (1.02)²⁹ ≈ 45,67,800 × 1.81 ≈ **82,77,600** (approximate). Alternatively, simple proportional increase: if we assume 50% growth over ~30 years, new population ≈ 45,67,800 × 1.5 ≈ **68,50,000**. [1.5 marks: estimation logic and calculation] (d) **Vinculum method for 12,34,567:** The vinculum places a bar over a numeral to multiply it by 1,000. So: - 12 with a bar = 12,000 - Remaining: 34,567 = 30,000 + 4,000 + 500 + 60 + 7 = XXX with bar + IV with bar + D + LX + VII - Full notation becomes: **X̄II̅M̅C̅C̅C̅C̅X̅X̅X̅IVDLXVII** (cumbersome and non-standard). **Why impractical:** (1) Handwriting becomes illegible. (2) No universal agreement on multi-bar notation. (3) Modern positional Hindu-Arabic system is infinitely more efficient. (4) Historical records used Roman numerals for dates and small quantities, not stock inventories. [2 marks: attempted notation + explanation of why modern systems are superior] **Total: 5 marks**

The CBSE Class 9 Mathematics syllabus for 2024–2025 retains Chapter 3 (Number Play) but with subtle emphasis shifts. Based on recent exam trends: (1) **Increased focus on real-world applications.** Questions now embed place value and rounding in contexts — e.g., 'A city census recorded 45,67,890 people. Estimate it to the nearest lakh for a report.' This tests conceptual understanding, not mere mechanics. (2) **Reduced emphasis on pure Roman numerals.** While conversion (Hindu-Arabic ↔ Roman) is still tested, questions involving Roman numerals now rarely exceed MMMCMXCIX (3,999). The focus is on recognition and small conversions, not complex constructions. (3) **Harder 'number puzzles.'** The 3-mark puzzles now include logical conditions (e.g., 'If my tens digit is 3 more than my hundreds digit and...'), testing reasoning alongside arithmetic. (4) **Estimation is a core skill.** Questions increasingly ask you to estimate first, then optionally verify with exact calculations. This mirrors real-world maths and engineering. (5) **Linkage to other chapters.** Number Play concepts now appear in Chapter 1 (Numbers) and Chapter 2 (Exponents), creating integrated problem sets. Expect questions like: 'Express 2³ × 5⁴ in expanded form and round the product to the nearest hundred.' (6) **Emphasis on clear communication.** Marks are increasingly awarded for explaining **why** you chose a rounding method, not just the answer. Write 'I rounded down because the digit in the next place is 2, which is < 5' — this earns a mark even if the final answer has a typo. (7) **Inclusivity of all numeration systems.** While Indian and International systems dominate, expect occasional references to binary (₂) or other bases as extension questions — still within Class 9 reach but stretching conceptual depth.

You have 2 hours for the entire Mathematics exam. Chapter 3 (Number Play) typically accounts for 8–10 marks (1–2 questions). Here's how to nail it: **Pre-exam (30 minutes before):** Skim all 13 solved questions above. Mentally note the traps: 'smallest 8-digit number starts with 1', 'place value ≠ face value', 'Roman numerals stop at ~4,000'. **During the exam (8–10 minutes allocated):** (1) If you see a 1-mark question first, solve it in 45 seconds. (2) If a 3-mark question appears, allocate 2.5 minutes: read carefully (30 sec), plan your approach (30 sec), solve (90 sec), check (30 sec). (3) If a 5-mark appears, allocate 5 minutes: spend 1 minute understanding what's asked, 3 minutes solving, 1 minute verifying. (4) **Avoid overwork.** If you're stuck on a 3-mark question after 2.5 minutes, mark it for review and move on. Your other answers matter more. (5) **Prioritize accuracy over speed.** A correct 3-mark answer is worth more than two rushed, incorrect 1-mark answers. (6) **Final check (2 minutes):** Reread your answers for typos. A ₹ sign missing or 'lakh' misspelled loses marks. **Mindset:** Number Play questions are 'safe' — they test technique, not tricks. If you've practised the 13 questions above, you'll recognize at least 70% of the real exam's wording. This is where you build confidence and push toward a high score. Start a 3-day free trial at cbsetutor.ai to access video walkthroughs of every one of these questions, plus adaptive quizzes that track your weak spots and adjust difficulty in real time.

**How do I remember the Indian vs. International naming system?** Indian: ones, tens, hundreds | thousands, ten thousands, lakhs | ten lakhs, crores. International: ones, tens, hundreds | thousands, ten thousands, hundred thousands | millions. A memory trick: In Indian, we use 'lakhs' and 'crores' — words unique to India. International uses standard 'million, billion.' Whenever you see a question, check if it says 'lakh' — if yes, use Indian naming. **What's the easiest way to check my rounding answer?** After rounding, ask: 'Is the digit I zeroed out less than 5?' If yes, keep the previous digit unchanged. If ≥ 5, increase the previous digit by 1. Example: 34,567 rounded to the nearest thousand. The digit in the hundreds place is 5 ≥ 5, so round up: 35,000. **Why do Roman numerals matter in Class 9 if I'll never use them in real life?** Great question. Roman numerals teach you: (1) alternative representation systems (useful in computer science), (2) historical literacy (you'll see them on clocks, book chapters, movie credits), (3) constraints of non-positional notation (why Hindu-Arabic is superior). It's about conceptual breadth. **How many marks does Chapter 3 typically carry?** 8–10 marks in a 100-mark exam. Usually: one 1-mark Q, one 3-mark Q, and partial weightage in a 5-mark multi-part Q. Rarely is an entire 5-mark question solely Number Play; it's often combined with Chapter 1 or 2. **Is estimation always required, or can I give exact answers?** Exact answers are always safer. Estimation is a shortcut for checking or when the question explicitly says 'estimate.' However, examiners reward estimation as a **method** — i.e., they value the thinking process. If a question asks 'estimate,' showing your rounding steps earns marks even if your final estimate is slightly off. **I keep confusing place value and face value. How do I remember?** Face value = the digit itself (always). Place value = digit × its position's multiplier. Example: In 3,45,000, the face value of 4 is 4, but its place value is 4 × 10,000 = 40,000. An analogy: a '₹100 note' has a face value of ₹100. But if it's in a 'thousand-rupee bundle,' it represents ₹100 in that context (place value within a system).