NCERT Solutions for CBSE Class 7 Mathematics Chapter 1: Large Numbers Around Us

The Indian place value system organizes numbers by grouping digits in a specific pattern: the first three digits from the right (ones, tens, hundreds), then pairs of digits separated by commas—thousands and ten-thousands, lakhs and ten-lakhs, crores and ten-crores, and so on. This ancient system, rooted in Vedic mathematics, remains the official standard across India for government reports, census data, economic indicators, and everyday commerce. In CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us, students learn to read numbers like 45,67,890 as 'forty-five lakh, sixty-seven thousand, eight hundred and ninety.' The placement of commas after every two digits (except the initial group of three) is non-negotiable—45,67,890 is correct; 4,567,890 would be International notation. Understanding this system is crucial because Indian newspapers report 'India's GDP crosses 200 lakh crores,' school budgets are framed in lakhs, and property prices are quoted in crores. NCERT emphasizes that one lakh equals 1,00,000 (five zeros) and one crore equals 1,00,00,000 (seven zeros). This knowledge allows students to decode headlines, compare financial figures, and appreciate the scale of national statistics. Real-world example: If a state government allocates 12,34,56,789 rupees for education, a Class 7 student using the Indian system reads this instantly as 'twelve crore, thirty-four lakh, fifty-six thousand, seven hundred and eighty-nine rupees'—a skill tested in CBSE exams through word problems and data interpretation questions.

NCERT introduces the International place value system in CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us to prepare students for global contexts—scientific literature, international trade data, English-language textbooks, and technology documentation all use this system. Here, numbers are grouped in threes from the right: ones, tens, hundreds | thousands | millions | billions | trillions. Commas appear after every three digits: 45,678,900 reads as 'forty-five million, six hundred and seventy-eight thousand, nine hundred.' One million equals 1,000,000 (six zeros), which is ten lakhs in the Indian system. One billion equals 1,000,000,000 (nine zeros), equivalent to one hundred crores. This conversion knowledge is essential—when NASA announces a Mars rover travelled 124 million kilometres, an Indian student must translate this to '12 crore, 40 lakh kilometres' to visualize the distance in familiar terms. CBSE Class 7 board exams frequently include conversion questions: 'Express 5 crores in the International system' or 'Convert 23 million to Indian notation.' The answer requires both systems: 5 crores = 5,00,00,000 = 50,000,000 = 50 million. Similarly, 23 million = 23,000,000 = 2,30,00,000 = 2 crores 30 lakhs. Mastering both systems gives students flexibility—they can read The New York Times ('Apple's market cap hits 3 trillion dollars') and Times of India ('Sensex crosses 70,000 crore market value') with equal fluency. NCERT includes practice exercises where students must rewrite the same number in both systems, reinforcing the equivalence of 10 lakhs and 1 million, 100 crores and 1 billion.

Place value is the foundational concept of CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us—it assigns a specific value to each digit based on its position in a number. In 5,67,89,012, the digit 5 sits in the crores place, so its value is 5 × 1,00,00,000 = 5,00,00,000. The digit 6 is in ten-lakhs place: 6 × 10,00,000 = 60,00,000. The digit 7 is in lakhs place: 7 × 1,00,000 = 7,00,000. Understanding place value allows instant mental comparison without full arithmetic. Is 8 crores greater than 95 lakhs? Yes—because crores occupy a higher place value than lakhs. Students do not need to expand; the position alone determines magnitude. NCERT emphasizes expanded form exercises: write 23,45,67,312 as (2 × 10,00,00,000) + (3 × 1,00,00,000) + (4 × 10,00,000) + (5 × 1,00,000) + (6 × 10,000) + (7 × 1,000) + (3 × 100) + (1 × 10) + (2 × 1). This decomposition reinforces that each position represents a power of ten. Place value errors cause calculation mistakes: if a student misreads 12,34,567 as 1,23,45,67 (wrong comma placement), they have introduced a ten-fold error. CBSE exam questions test place value through fill-in-the-blanks ('The place value of 8 in 5,08,34,210 is ___'), multiple-choice identification, and word problems requiring digit extraction. Real-world application: In a population figure of 78,45,32,156, each digit conveys precise information—7 means seventy million people in International terms or seven ten-crores in Indian. Understanding place value is the gateway to all higher mathematics involving decimals, scientific notation, and algebra.

NCERT Solutions for CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us emphasize accurate reading and writing as foundational skills. Reading a number aloud in Indian system requires identifying each place group: for 23,45,67,312, break it as 23 crores | 45 lakhs | 67 thousands | 312 ones, then read: 'twenty-three crore, forty-five lakh, sixty-seven thousand, three hundred and twelve.' Omitting any place name or misplacing 'lakh' and 'thousand' leads to errors. Writing from words to figures demands reverse engineering: given 'Fifty-six crore, seventy-eight lakh, ninety thousand, one hundred and twenty-three,' students must parse each component—56 crores = 56,00,00,000, 78 lakhs = 78,00,000, 90 thousands = 90,000, 123 = 123—then sum them: 56,78,90,123. CBSE exams allocate 2-3 marks per reading/writing question, testing both systems. A typical question: 'Write in words using the International system: 234,567,890.' Answer: 'Two hundred thirty-four million, five hundred sixty-seven thousand, eight hundred and ninety.' Students must avoid Indian place names here. Another common question: 'Write the smallest and largest 8-digit numbers using digits 0-9 without repetition, then read them in Indian system.' Solution requires arranging digits (smallest: 10,234,567; largest: 98,765,432) and correct reading. NCERT practice pages include 20+ such exercises to build fluency. Real-world context: When news reports 'Government allocates 1,25,34,56,789 rupees,' students trained in CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us can instantly read it as 'one hundred twenty-five crore, thirty-four lakh, fifty-six thousand, seven hundred and eighty-nine rupees,' demonstrating numerical literacy.

Comparing large numbers systematically is a core skill in CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us. NCERT teaches a three-step method: (1) Count the number of digits—more digits generally means a larger number (exception: different systems). (2) If digit counts are equal, compare digit-by-digit from leftmost (highest place value) to right. (3) The first position where digits differ determines the larger number. Example: Compare 5,67,89,123 and 5,67,90,000. Both have 8 digits. Compare from left: 5=5, 6=6, 7=7, 8=9. Here 8 < 9, so 5,67,89,123 < 5,67,90,000. Ordering (ascending or descending) requires comparing multiple numbers and arranging them. CBSE exam questions often ask: 'Arrange in ascending order: 56,78,90,000; 5,67,89,123; 5,67,90,000; 56,78,89,456.' Solution: First, group by digit count—7-digit, 8-digit, 9-digit. Ascending means smallest first: 5,67,90,000 (7 digits) < 5,67,89,123 (8 digits) < 56,78,89,456 (9 digits) < 56,78,90,000 (9 digits). For the two 9-digit numbers, compare digit-by-digit: 56,78,89,456 vs 56,78,90,000 → at position 7 from left, 8 < 9, so 56,78,89,456 comes first. Final order: 5,67,90,000, 5,67,89,123, 56,78,89,456, 56,78,90,000. NCERT includes exercises where students must identify the greatest and smallest from a set, use symbols (<, >, =), and explain their reasoning. Real-world application: Comparing populations of Indian cities (Delhi: 3,00,00,000 vs Mumbai: 2,50,00,000) or state budgets helps students make sense of civic data. This skill also prepares students for data handling chapters in Class 8, where interpreting bar graphs and tables requires quick numerical comparisons.

Estimation is a practical mathematical skill emphasized in CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us. It involves finding an approximate value by rounding to a convenient place value—nearest ten, hundred, thousand, lakh, or crore. NCERT explains estimation's real-world importance: exact precision is often unnecessary or impossible (e.g., estimating crowd size at a rally, quick budget checks, rough distance calculations). The standard rounding rule: look at the digit immediately to the right of the place you are rounding to. If it is 5 or greater, round up (add 1 to the rounding place); if less than 5, round down (keep the rounding place as is), and replace all digits to the right with zeros. Example: Round 56,78,456 to the nearest lakh. The lakhs place digit is 6. The digit to its right (ten-thousands place) is 7. Since 7 ≥ 5, round up: 6 becomes 7. Replace digits to the right with zeros: 57,00,000. So 56,78,456 ≈ 57,00,000 (approximately 57 lakhs). CBSE exams test this with questions like 'Estimate the sum of 45,67,890 and 23,45,678 by rounding both to nearest lakh.' Solution: 45,67,890 ≈ 46,00,000; 23,45,678 ≈ 23,00,000. Estimated sum = 46,00,000 + 23,00,000 = 69,00,000. Actual sum is 69,13,568, so estimation is close and useful for mental math checks. Estimation also appears in word problems: 'A district has 8,76,543 people. Estimate to the nearest ten thousand.' Answer: Ten-thousands digit is 7; digit to right is 6 (≥5), so round up to 8,80,000. This skill prevents silly errors—if a student calculates an exact answer wildly different from their estimate, they know to re-check their work.

Successor and predecessor are simple yet frequently tested concepts in CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us. The successor of a number is the number that comes immediately after it—obtained by adding 1. The predecessor is the number immediately before—obtained by subtracting 1. For 99, successor is 100; predecessor is 98. For large numbers: successor of 1,00,00,000 (1 crore) is 1,00,00,001; predecessor is 99,99,999. NCERT includes these terms because they test understanding of place value transitions—when 99,99,999 becomes 1,00,00,000, all digits reset and a new place (crores) is created. CBSE exam questions: 'Write the successor of the largest 7-digit number.' Largest 7-digit number is 99,99,999; successor is 99,99,999 + 1 = 1,00,00,000 (which is actually an 8-digit number). Another type: 'Find the predecessor of 10,00,000 (ten lakh).' Answer: 10,00,000 − 1 = 9,99,999. These questions carry 1-2 marks and test careful attention to digit transitions. Predecessor-successor understanding also helps in subtraction problems involving borrowing across multiple zeros. Real-world interpretation: If a city's population is exactly 10,00,000, the predecessor (9,99,999) represents the population one person ago, and successor (10,00,001) is one person later. While abstract, this thinking trains precision—important for coding, data analysis, and logical reasoning in higher mathematics.

System conversion is a high-frequency question type in CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us. NCERT provides conversion practice because students encounter both systems in textbooks, news, and online content. The key conversions to memorize: 1 lakh = 1,00,000; 1 crore = 1,00,00,000; 1 million = 10,00,000 (10 lakhs); 1 billion = 1,00,00,00,000 (100 crores). Conversion process: (1) Write the number without commas. (2) Re-insert commas according to the target system's rules. (3) Read in the new system's terminology. Example: Convert 3 crores 25 lakhs to International. Step 1: Write in full: 3,25,00,000. Step 2: Remove commas: 32500000. Step 3: Place International commas (every three digits from right): 32,500,000. Step 4: Read: thirty-two million, five hundred thousand (or 32.5 million). Reverse example: Convert 45 million to Indian system. Step 1: Write 45,000,000. Step 2: Place Indian commas: 4,50,00,000. Step 3: Read: 4 crores 50 lakhs. CBSE exam questions worth 3-4 marks: 'India's population is approximately 140 crores. Express this in the International system and in standard numeral form.' Answer: 140 crores = 140,00,00,000 (Indian) = 1,400,000,000 (International) = 1.4 billion. Students must show all steps for full marks. Conversion errors often arise from incorrect comma placement—writing 1,40,00,00,000 (which has wrong grouping) instead of 1,40,00,00,000 (correct Indian) or 1,400,000,000 (correct International). NCERT practice exercises include 15+ conversion problems to build fluency.

NCERT textbook exercises for CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us span multiple pages and cover all concepts—reading, writing, comparing, ordering, rounding, and system conversion. Exercise 1.1 focuses on identifying and writing place values: 'Write the place value of each digit in 5,67,89,012.' Solution requires expanded form: (5 × 1,00,00,000) + (6 × 10,00,000) + (7 × 1,00,000) + (8 × 10,000) + (9 × 1,000) + (0 × 100) + (1 × 10) + (2 × 1). Exercise 1.2 includes comparison and ordering: 'Arrange in descending order: 23,45,678; 2,34,56,780; 2,34,567.' Solution: Count digits—8, 9, 7. Largest is 9-digit (2,34,56,780), then 8-digit (23,45,678), then 7-digit (2,34,567). Exercise 1.3 covers rounding: 'Round 6,78,45,923 to the nearest ten lakh.' Ten-lakhs digit is 7; digit to right (lakhs) is 8 (≥5), so round up: 7 becomes 8. Answer: 6,80,00,000. Exercise 1.4 deals with word problems: 'The population of City A is 45,67,890 and City B is 56,78,900. Which city has a larger population and by how much?' Solution: Compare—56,78,900 > 45,67,890. Difference: 56,78,900 − 45,67,890 = 11,11,010. City B is larger by 11 lakh, 11 thousand and 10. Exercise 1.5 involves conversions: 'Express 5 crores in the International system.' 5 crores = 5,00,00,000 = 50,000,000 = 50 million. NCERT also includes application problems: 'A state's annual budget is 1,23,45,67,890 rupees. Round to the nearest crore and express in words.' Nearest crore: 1,23,00,00,000 = one hundred twenty-three crores. Students preparing for CBSE exams should solve every NCERT exercise question at least twice—once for learning, once for speed and accuracy under timed conditions. Model answers and step-by-step solutions are available in NCERT exemplar and guidebooks, but working through independently builds deeper understanding.

CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us is not abstract—it connects directly to real-world data students encounter daily. India's population (approximately 140 crores or 1.4 billion) is a large number requiring both systems for interpretation. Government budgets, reported in 'lakh crores,' demand understanding: India's 2024-25 Union Budget is approximately 48 lakh crores (48,00,00,00,00,000 rupees or 48 trillion rupees internationally). Students must parse such figures to participate in informed civic discussions. Geographic data: India's land area is approximately 32,87,263 square kilometres (32 lakh, 87 thousand, 263 sq km)—comparing this to other countries' areas requires ordering large numbers. Economic indicators: India's GDP is reported as $3.7 trillion internationally or approximately 370 lakh crores in rupees. Sports statistics: IPL cricket franchises are valued in thousands of crores; understanding these valuations requires comfort with large numbers. Environmental data: Annual carbon emissions, water usage in billions of litres, forest cover in lakh hectares—all involve large number literacy. NCERT embeds such real-world contexts in word problems to make learning relevant. For instance, a typical question: 'India produced 3,25,67,89,000 kg of wheat in 2023. Express this in crores of kg and round to nearest crore.' Solution: 3,25,67,89,000 kg = 325.67 crore kg ≈ 326 crore kg. This bridges mathematics with current affairs, economics, and science. Students who master CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us find themselves better equipped to read newspapers critically, understand financial planning at home, and interpret data in higher classes—statistics, probability, and data science all assume fluency with large numbers.

Students often make predictable errors in CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us—recognizing these helps avoid mark loss in exams. Mistake 1: Confusing lakh with million. Students write '1 lakh = 1 million,' but 1 lakh = 100,000 while 1 million = 1,000,000. Correct conversion: 1 million = 10 lakhs. Mistake 2: Incorrect comma placement. Writing 12,34,567 in International system when it should be 1,234,567 (three-digit grouping). Or writing International number 1,234,567 with Indian commas as 12,34,567. Each system has strict rules. Mistake 3: Forgetting to check tens digit when rounding. Rounding 78,45,678 to nearest lakh: students look at lakhs digit (4) and round down to 78,00,000. Wrong. Must check the digit to the right of lakhs (ten-thousands = 5), which is ≥5, so round up to 78,50,000. Wait—actually, rounding to nearest lakh means looking at ten-thousands digit: here 4 (next is 5, but we round the lakh itself). Actually: lakhs place is 4, ten-thousands is 5. Since 5≥5, round up: 4 becomes 5. Answer: 78,50,000. Mistake 4: Misinterpreting word problems. 'Population increased by 5 lakhs' vs 'population is 5 lakhs'—students conflate absolute values with differences. Mistake 5: Writing expanded form incorrectly—forgetting to multiply each digit by its place value. In 5,67,890, writing (5 + 6 + 7 + 8 + 9 + 0) instead of (5×1,00,000) + (6×10,000) +.... Mistake 6: Assuming more digits always means larger—true within one system, but 99,99,999 (Indian 7-digit) equals 9,999,999 (International 7-digit); same number, different notation. Mistake 7: Calculation errors in conversion—adding zeros incorrectly when converting crores to millions. 5 crores = 50 million, not 5 million (common mistake: forgetting that 1 crore = 10 million). Practicing NCERT exercises thoroughly and reviewing worked solutions prevents these errors.

CBSE Class 7 annual exams allocate approximately 8-10 marks to CBSE Class 7 Mathematics Chapter 1 Large Numbers Around Us, distributed across question types: 2-3 objective questions (1 mark each, MCQ or fill-in-the-blank), 2-3 short-answer questions (2 marks each, requiring one-step calculation or direct application), and 1-2 long-answer questions (3-4 marks, multi-step problems or word problems). Objective questions test recall: 'One crore equals how many lakhs?' (Answer: 100 lakhs—1 mark). Fill-in-the-blank: 'The place value of 7 in 5,67,89,012 is ___' (Answer: 7,00,000—1 mark). Short-answer (2 marks): 'Arrange in ascending order: 5,67,890; 56,78,900; 5,67,900.' Solution requires comparison steps (1 mark) and correct final order (1 mark). Long-answer (4 marks): 'A state has three districts with populations 12,34,567; 23,45,678; and 34,56,789. (a) Find total population. (b) Round each to nearest lakh. (c) Express total in International system.' Solution: (a) Sum = 70,36,034 (1 mark). (b) Rounded: 12,00,000 + 23,00,000 + 35,00,000 (1 mark for correct rounding). (c) 70,36,034 = 7,036,034 (International) = 7.036 million (1 mark for conversion, 1 mark for reading). Marking scheme awards partial credit—showing method even with calculation error earns 1-2 marks. Strategy: Read each question carefully, underline key terms (ascending, nearest lakh, International system), show all steps clearly, box final answers, and verify by re-reading the question. Time management: allocate 1 minute per mark (1-mark question = 1 minute, 4-mark question = 4 minutes). Reserve 5 minutes at the end for review—catch silly errors like missing commas or wrong place names. Practicing past CBSE papers and sample papers familiarizes students with question phrasing and difficulty level. NCERT exemplar problems are slightly harder—ideal for advanced practice. Students scoring 8+ marks in this chapter find subsequent chapters (integers, fractions) easier because place value understanding transfers directly.

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