Class 9 Mathematics Chapter 1: Large Numbers Around Us – Important Questions with Solutions

Chapter 1 sets the foundation for all arithmetic in Class 9 and beyond. CBSE's 2024-25 rationalized syllabus emphasizes conceptual understanding over rote learning, meaning examiners now test your ability to work across number systems and estimate real-world quantities. The board pattern increasingly includes mixed-format questions that require you to convert between Indian (lakh, crore) and International (million, billion) systems, compare magnitudes, and justify estimation choices. Questions on place value extension appear not just as definition-recall, but as problem-solving scenarios—for example, determining digit positions in population statistics or astronomical numbers. Understanding standard form (or scientific notation basics) and the logic behind grouping digits is tested across short-answer and long-answer sections. Moreover, these skills directly enable success in data handling, statistics, and even physics chapters that follow. A student who confidently reads and interprets '2.56 crore' or '1.8 billion' avoids costly errors in real-world applications and higher-level problem solving.

**Q1.** Which of the following is equivalent to 1 crore? (A) 10⁵ (B) 10⁶ (C) 10⁷ (D) 10⁸ **Answer:** (C) 10⁷ *Explanation:* 1 crore = 10 million = 1,00,00,000 = 10⁷. This is the Indian system's largest standard unit before the lakh. **Q2.** How many millions make 1 billion? (A) 100 (B) 1,000 (C) 10,000 (D) 100,000 **Answer:** (B) 1,000 *Explanation:* 1 billion (International system) = 1,000,000,000 = 1,000 × 10⁶ = 1,000 million. **Q3.** The place value of 7 in 5,74,23,189 (Indian system) is: (A) 7 lakhs (B) 70 lakhs (C) 7 crores (D) 70 crores **Answer:** (B) 70 lakhs *Explanation:* Reading from right: 9 (ones), 8 (tens), 1 (hundreds), 3 (thousands), 2 (ten-thousands), 4 (lakhs), 7 (ten-lakhs) = 70 lakhs. **Q4.** Express 3.5 million in the Indian system: (A) 35 lakhs (B) 3.5 lakhs (C) 350 lakhs (D) 0.35 crores **Answer:** (A) 35 lakhs *Explanation:* 1 million = 10 lakhs, so 3.5 million = 3.5 × 10 = 35 lakhs. **Q5.** In standard form, 4,50,00,000 is written as: (A) 4.5 × 10⁶ (B) 4.5 × 10⁷ (C) 45 × 10⁶ (D) 0.45 × 10⁸ **Answer:** (B) 4.5 × 10⁷ *Explanation:* 4,50,00,000 = 4.5 × 1,00,00,000 = 4.5 × 10⁷ (moving decimal 7 places).

**Q1.** Write 72 lakhs 45 thousand 89 in expanded form (Indian system). Also, express it as a standard form number. **Solution:** 72 lakhs 45 thousand 89 = 72,45,089 Expanded form: 7 × 10⁶ + 2 × 10⁵ + 4 × 10⁴ + 5 × 10³ + 0 × 10² + 8 × 10¹ + 9 × 10⁰ Standard form: 7.245089 × 10⁶ **Q2.** A country's population is 1.42 billion. Express this in the Indian number system (crores and lakhs). **Solution:** 1.42 billion = 1.42 × 10⁹ = 14,20,00,000 (fourteen crore twenty lakh) Or: 1.42 billion = 14.2 crores = 142 crores (approximately) **Q3.** Compare 5 crores and 45 million. Which is larger? **Solution:** 5 crores = 5 × 10⁷ = 50 million Therefore, 5 crores (50 million) > 45 million by 5 million. **Q4.** Round 3,68,74,529 to the nearest crore and the nearest lakh. **Solution:** 3,68,74,529 Nearest crore: 3,70,00,000 (since 68,74,529 > 50,00,000, round up) Nearest lakh: 3,68,75,000 (since 4,529 > 50,000, round up) **Q5.** If the digit 6 occupies the ten-lakh place, what is its place value? Give an example number. **Solution:** Place value of 6 in ten-lakh place = 6 × 10⁶ = 60,00,000 (sixty lakh) Example: 2,65,43,215 where 6 is in the ten-lakh place.

**Q1.** A factory produces 2.5 million items per year. How many items does it produce in 8 years? Express your answer in the Indian system (crores and lakhs). **Solution:** Items in 8 years = 2.5 × 10⁶ × 8 = 20 × 10⁶ = 2 × 10⁷ = 2 crores Answer: 2 crores (or 20 million) items. **Q2.** Complete the conversion table below: | Indian System | International System | |---|---| | 1 Lakh | ? | | ? | 1 Million | | 1 Crore | ? | | ? | 1 Billion | **Solution:** | Indian System | International System | |---|---| | 1 Lakh | 0.1 Million | | 10 Lakhs | 1 Million | | 1 Crore | 10 Million | | 100 Crores | 1 Billion | **Q3.** A scientist measures the mass of an atom as 0.0000000000000000000000166 grams. Express this in standard form and explain the place value of the non-zero digit. **Solution:** 0.0000000000000000000000166 = 1.66 × 10⁻²⁴ grams The digit 1 occupies the 10⁻²⁴ place (a value 24 places to the right of the decimal). This demonstrates how place value extends beyond large numbers into the microscopic scale, showing the universality of our number system. **Q4.** A country spends 5 crores on education and 8 million on health. What is the total expenditure? If the budget is 20 crores, what percentage remains unspent? **Solution:** 5 crores = 50 million Total expenditure = 50 million + 8 million = 58 million = 5.8 crores Remaining budget = 20 crores − 5.8 crores = 14.2 crores Percentage unspent = (14.2 / 20) × 100 = 71%

**Q1.** Two numbers are written as 3.6 × 10⁷ and 4.2 × 10⁶. (i) Express both in the Indian number system (crores and lakhs). (ii) Find their sum and express the result in standard form. (iii) Which number is larger, and by how much? **Full Solution:** (i) First number: 3.6 × 10⁷ = 36,000,000 = 3 crores 60 lakhs Second number: 4.2 × 10⁶ = 4,200,000 = 42 lakhs (ii) Sum = 36,000,000 + 4,200,000 = 40,200,000 = 4.02 × 10⁷ (iii) Difference = 36,000,000 − 4,200,000 = 31,800,000 = 3.18 × 10⁷ The first number (3.6 × 10⁷) is larger by 31.8 lakh (or 3.18 crore). --- **Q2.** A city's population in 2020 was 82.5 lakh. If it grows at a rate of 2.5% annually, estimate the population in 2025 (i.e., after 5 years). Express your answer in both Indian and International systems. **Full Solution:** Initial population (P₀) = 82.5 lakh = 8,250,000 Growth rate (r) = 2.5% per annum Number of years (t) = 5 Using estimation (since exact compound interest is Grade 10 level): Year 1: 8,250,000 + (2.5% of 8,250,000) = 8,250,000 + 206,250 = 8,456,250 Year 2: 8,456,250 + (2.5% of 8,456,250) ≈ 8,667,656 Year 3: ≈ 8,884,547 Year 4: ≈ 9,106,961 Year 5: ≈ 9,334,936 Estimated population in 2025 ≈ 93.3-94 lakh ≈ 9.3-9.4 million Or, using simple approximation: 82.5 + (5 × 2.5% of 82.5) ≈ 82.5 + 10.3 ≈ 92.8 lakh **Answer:** Approximately 93 lakh (or 9.3 million) in 2025. --- **Q3.** A publishing house prints books. They print 5 crore pages of textbooks and 3.5 crore pages of fiction. Each page costs ₹0.50 to print. (i) Find the total number of pages printed (in millions and standard form). (ii) Calculate the total cost of printing. (iii) If they earn ₹1.25 per page sold, what is the profit or loss (assume all books are sold)? **Full Solution:** (i) Total pages = 5 crore + 3.5 crore = 8.5 crore = 85 million = 8.5 × 10⁷ pages (ii) Total cost = 8.5 crore pages × ₹0.50 per page = 8.5 × 10⁷ × 0.50 = 4.25 × 10⁷ = ₹4 crore 25 lakh (iii) Total revenue = 8.5 crore pages × ₹1.25 per page = 8.5 × 10⁷ × 1.25 = 10.625 × 10⁷ = ₹10 crore 62.5 lakh Profit = ₹10 crore 62.5 lakh − ₹4 crore 25 lakh = ₹6 crore 37.5 lakh = ₹6.375 crore **Answer:** Total profit is ₹6 crore 37.5 lakh (or ₹63.75 million).

**Case Study: Global Population Statistics** A UN report provides the following population data (in billions): - Asia: 4.64 billion - Africa: 1.37 billion - Europe: 0.75 billion - Americas: 1.04 billion - Oceania: 0.044 billion **Questions:** (i) Convert the population of each continent into the Indian number system (crores). (ii) Rank the continents by population (largest to smallest). (iii) What is the total global population? Express it in crores, millions, and standard form. (iv) Asia's population is how many times the population of Oceania? Estimate to 1 decimal place. (v) If Africa's population grows by 3% per year, estimate how many crores of people will be added in one year. **Step-by-Step Solution:** **Step 1:** Convert billions to crores (1 billion = 100 crores) - Asia: 4.64 × 100 = 464 crores - Africa: 1.37 × 100 = 137 crores - Europe: 0.75 × 100 = 75 crores - Americas: 1.04 × 100 = 104 crores - Oceania: 0.044 × 100 = 4.4 crores **Step 2:** Rank from largest to smallest 1. Asia (464 crores) 2. Africa (137 crores) 3. Americas (104 crores) 4. Europe (75 crores) 5. Oceania (4.4 crores) **Step 3:** Total global population Sum = 464 + 137 + 104 + 75 + 4.4 = 784.4 crores = 78.44 × 10⁸ crores (or approximately 78-79 crores × 10⁸) = 7,844 million (or 7.844 billion) = 7.844 × 10⁹ (standard form) **Step 4:** Asia ÷ Oceania ratio 464 ÷ 4.4 = 105.45 ≈ 105.5 Asia's population is approximately **105.5 times** that of Oceania. **Step 5:** Annual population growth in Africa 3% of 137 crores = 0.03 × 137 = 4.11 crores Therefore, approximately **4.1 crores** people will be added to Africa's population in one year. **Why This Question Matters:** It integrates number-system conversion, real-world data interpretation, ranking, ratio analysis, and percentage estimation—all key Class 9 skills.

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