This MCQ module is based on: Crore, Estimation and Population Data
Crore, Estimation and Population Data
This mathematics assessment will be based on: Crore, Estimation and Population Data
Targeting Class 7 level in Number Theory, with Basic difficulty.
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1.3 Of Crores and Crores!
In Part 1, we used a Button Calculator with buttons like +1, +10, +100, ..., +10,00,000. What happens if we press the +10,00,000 button ten times?
Pressing +10,00,000 ten times on the button calculator gives 1,00,00,000 = One Crore.
- 1 Crore = 100 Lakhs
- 1 Crore = 1,00,00,000 (1 followed by 7 zeroes)
- The word crore comes from the Sanskrit word koṭi (कोटि)
- The word lakh comes from the Sanskrit word lakṣha (लक्ष)
Indian System vs. American (International) System
The same number is written and named differently in the Indian System? and the International System?. The key difference lies in how commas are placed:
Groups: Thousands, Lakhs, Crores, Arabs.
Used in India, Nepal, Bhutan, Sri Lanka, Pakistan, Bangladesh, Myanmar, Afghanistan, and Maldives.
Groups: Thousands, Millions, Billions.
Used in the USA and many other countries.
| Indian Notation | Indian Name | International Notation | International Name |
|---|---|---|---|
| 1,000 | One thousand | 1,000 | One thousand |
| 10,000 | Ten thousand | 10,000 | Ten thousand |
| 1,00,000 | One lakh | 100,000 | Hundred thousand |
| 10,00,000 | Ten lakhs | 1,000,000 | One million |
| 1,00,00,000 | One crore | 10,000,000 | Ten million |
| 10,00,00,000 | Ten crores | 100,000,000 | Hundred million |
| 1,00,00,00,000 | One arab (= 100 crores) | 1,000,000,000 | One billion |
1 Lakh = 1 followed by 5 zeroes | 1 Crore = 1 followed by 7 zeroes
A thousand lakhs = 1 crore. A hundred crores = 1 arab. A thousand thousand lakh = how many zeroes? Count: 3 + 3 + 5 = 11 zeroes → That's 100 arabs!
How many zeroes does a thousand lakh have?
1000 = 10³ and 1 lakh = 10⁵, so thousand lakh = 10³ × 10⁵ = 10⁸ → 8 zeroes.
How many zeroes does a hundred thousand have? 100,000 = 10⁵ → 5 zeroes.
Reading a Large Number Both Ways
Consider the number 9876501234. Placing commas reveals its value clearly:
Type any whole number (up to 10 digits) and see its name in both naming systems instantly.
📝 Figure it Out — Crores & Naming Systems
(a) 4050678 (b) 48121620 (c) 20022002 (d) 246813579 (e) 345000543 (f) 1020304050
| Number | Indian Notation | Indian Name | International Name |
|---|---|---|---|
| 40,50,678 | 40,50,678 | Forty lakh fifty thousand six hundred seventy-eight | Four million fifty thousand six hundred seventy-eight |
| 4,81,21,620 | 4,81,21,620 | Four crore eighty-one lakh twenty-one thousand six hundred twenty | Forty-eight million one hundred twenty-one thousand six hundred twenty |
| 2,00,22,002 | 2,00,22,002 | Two crore twenty-two thousand two | Twenty million twenty-two thousand two |
| 24,68,13,579 | 24,68,13,579 | Twenty-four crore sixty-eight lakh thirteen thousand five hundred seventy-nine | Two hundred forty-six million eight hundred thirteen thousand five hundred seventy-nine |
| 34,50,00,543 | 34,50,00,543 | Thirty-four crore fifty lakh five hundred forty-three | Three hundred forty-five million five hundred forty-three |
| 1,02,03,04,050 | 1,02,03,04,050 | One arab two crore three lakh four thousand fifty | One billion twenty million three hundred four thousand fifty |
(a) One crore one lakh one thousand ten
(b) One billion one million one thousand one
(c) Ten crore twenty lakh thirty thousand forty
(d) Nine billion eighty million seven hundred thousand six hundred
(a) 1 crore = 1,00,00,000; 1 lakh = 1,00,000; 1 thousand = 1,000; ten = 10
Total = 1,00,00,000 + 1,00,000 + 1,000 + 10 = 1,01,01,010
(b) 1 billion = 1,00,00,00,000 (= 100 crore); 1 million = 10 lakhs = 10,00,000; 1 thousand = 1,000; one = 1
Total = 1,00,10,01,001
(c) 10 crore = 10,00,00,000; 20 lakh = 20,00,000; 30 thousand = 30,000; forty = 40
Total = 10,20,30,040
(d) 9 billion = 9,00,00,00,000; 80 million = 8,00,00,000; 700 thousand = 7,00,000; 600 = 600
Total = 9,08,07,00,600
(a) 30 thousand ____ 3 lakhs
(b) 500 lakhs ____ 5 million
(c) 800 thousand ____ 8 million
(d) 640 crore ____ 60 billion
(a) 30,000 vs 3,00,000 → 30 thousand < 3 lakhs → <
(b) 500 lakhs = 5,00,00,000; 5 million = 50,00,000. So 500 lakhs > 5 million → >
(c) 800 thousand = 8,00,000; 8 million = 80,00,000. So 800 thousand < 8 million → <
(d) 640 crore = 6,40,00,00,000; 60 billion = 60,00,00,00,000. So 640 crore < 60 billion → <
1.4 Exact and Approximate Values
Have you ever noticed how newspapers report numbers? Consider this conversation:
According to the 2011 census, the population of Chintamani town is 76,068. Saying the population is about 75,000 gives a quick sense of the town's size — and that approximation is often sufficient.
Rounding Up vs. Rounding Down
The approximated number is more than the actual number.
Example: A school has 732 people. The principal orders 750 sweets (rounded up) so nobody is left out.
The approximated number is less than the actual number.
Example: An item costs ₹470. The shopkeeper says it is about ₹450 (rounded down) to sound like a bargain.
Identify situations where it is appropriate to:
- Round up — e.g. when buying enough supplies for everyone.
- Round down — e.g. when estimating how much money you will save.
- Either is okay — e.g. reporting approximate distances in geography.
- Exact numbers are needed — e.g. medicine doses, bank transactions, roll numbers.
Nearest Neighbours of a Large Number
With large numbers, it is useful to find the nearest neighbours? — i.e., the nearest thousand, nearest lakh, nearest crore, etc.
For example, the five nearest neighbours of 6,72,85,183 are:
| Rounded to | Nearest Neighbour | Rule Applied |
|---|---|---|
| Nearest Thousand | 6,72,85,000 | Last 3 digits = 183 < 500 → round down |
| Nearest Ten Thousand | 6,72,90,000 | Last 4 digits = 5,183 ≥ 5,000 → round up |
| Nearest Lakh | 6,73,00,000 | 85,183 ≥ 50,000 → round up |
| Nearest Ten Lakh | 6,70,00,000 | 2,85,183 < 5,00,000 → round down |
| Nearest Crore | 7,00,00,000 | 72,85,183 ≥ 50,00,000 → round up |
(a) 3,87,69,957 (b) 29,05,32,481
Also: I have a number whose all five nearest neighbours are 5,00,00,000. What could the number be? How many such numbers are there?
(a) 3,87,69,957:
- Nearest thousand: last 3 digits 957 ≥ 500 → round up → 3,87,70,000
- Nearest ten thousand: 9,957 ≥ 5,000 → round up → 3,87,70,000
- Nearest lakh: 69,957 ≥ 50,000 → round up → 3,88,00,000
- Nearest ten lakh: 7,69,957 ≥ 5,00,000 → round up → 3,90,00,000
- Nearest crore: 87,69,957 ≥ 50,00,000 → round up → 4,00,00,000
(b) 29,05,32,481:
- Nearest thousand: 481 < 500 → round down → 29,05,32,000
- Nearest ten thousand: 2,481 < 5,000 → round down → 29,05,30,000
- Nearest lakh: 32,481 < 50,000 → round down → 29,05,00,000
- Nearest ten lakh: 5,32,481 ≥ 5,00,000 → round up → 29,10,00,000
- Nearest crore: 9,05,32,481 < 50,00,00,000 ... wait, 9,05,32,481 ≥ 50,00,000? Yes! → round up → 30,00,00,000
All five neighbours = 5,00,00,000:
For nearest crore = 5,00,00,000: number must be between 4,50,00,001 and 5,49,99,999.
For nearest ten lakh = 5,00,00,000: number must be between 4,95,00,001 and 5,04,99,999.
For nearest lakh = 5,00,00,000: number must be between 4,99,50,001 and 5,00,49,999.
For nearest ten thousand = 5,00,00,000: must be between 4,99,95,001 and 5,00,04,999.
For nearest thousand = 5,00,00,000: must be between 4,99,99,501 and 5,00,00,499.
The intersection is: 4,99,99,501 to 5,00,00,499 — that's 999 numbers in total.
Enter any number to find its nearest thousand, ten-thousand, lakh, ten-lakh, and crore.
Math Talk — Estimation Challenge
Roxie and Estu are practising estimation. They evaluate the reasonableness of their estimates before calculating the exact answer.
Roxie: "The sum is near 8,00,000 and is more than 8,00,000."
Estu: "The sum is near 9,00,000 and is less than 9,00,000."
(a) Are these estimates correct? Whose estimate is closer?
(b) Will the sum be greater or less than 8,50,000? Why?
(c) Will the sum be greater or less than 8,83,128? Why?
(d) Find the exact value.
(a) 4,63,128 ≈ 5 lakh; 4,19,682 ≈ 4 lakh → sum ≈ 9 lakh.
Roxie says "near 8 lakh and more" — this is a valid lower estimate but not very close.
Estu says "near 9 lakh and less" — this is closer to the actual answer. Estu's estimate is closer.
(b) 4,63,128 > 4,25,000 and 4,19,682 > 4,25,000. So the sum > 8,50,000. Greater than 8,50,000.
(c) 4,63,128 + 4,19,682 vs 8,83,128. The second number in our sum is 4,19,682 < 4,20,000. So sum < 4,63,128 + 4,20,000 = 8,83,128. Less than 8,83,128.
(d) 4,63,128 + 4,19,682 = 8,82,810.
Roxie: "The difference is near 10,00,000 and is less than 10,00,000."
Estu: "The difference is near 9,00,000 and is more than 9,00,000."
(a) Are these estimates correct? Whose is closer?
(b) Greater or less than 9,50,000? Why?
(c) Greater or less than 9,63,128? Why?
(d) Find the exact value.
(a) 14,63,128 − 4,90,020 ≈ 15 lakh − 5 lakh = 10 lakh.
Roxie: "near 10 lakh, less than 10 lakh" ✔ (since we subtracted a bit less than 5 lakh from slightly less than 15 lakh).
Estu: "near 9 lakh, more than 9 lakh" ✔ (also valid).
Both estimates are in the right range. Roxie's is closer.
(b) 4,90,020 < 5,13,128 → difference > 14,63,128 − 5,13,128 = 9,50,000. Greater than 9,50,000.
(c) 14,63,128 − 4,90,020 vs 9,63,128 → subtract 4,90,020 from 14,63,128. Since 4,90,020 < 5,00,000, the difference is > 9,63,128. Greater than 9,63,128.
(d) 14,63,128 − 4,90,020 = 9,73,108.
Populations of Indian Cities (Census 2011)
Study the populations of India's top 20 cities (as per the 2011 census) and answer the questions below.
| Rank | City | Population 2011 | Population 2001 |
|---|---|---|---|
| 1 | Mumbai | 1,24,42,373 | 1,19,78,450 |
| 2 | New Delhi | 1,10,07,835 | 98,79,172 |
| 3 | Bengaluru | 84,25,970 | 43,01,326 |
| 4 | Hyderabad | 68,09,970 | 36,37,483 |
| 5 | Ahmedabad | 55,70,585 | 35,20,085 |
| 6 | Chennai | 46,81,087 | 43,43,645 |
| 7 | Kolkata | 44,86,679 | 45,72,876 |
| 8 | Surat | 44,67,797 | 24,33,835 |
| 9 | Vadodara | 35,52,371 | 16,90,000 |
| 10 | Pune | 31,15,431 | 25,38,473 |
| 11 | Jaipur | 30,46,163 | 23,22,575 |
| 12 | Lucknow | 28,15,601 | 21,85,927 |
| 13 | Kanpur | 27,67,031 | 25,51,337 |
| 14 | Nagpur | 24,05,665 | 20,52,066 |
| 15 | Indore | 19,60,631 | 14,74,968 |
| 16 | Thane | 18,18,872 | 12,62,551 |
| 17 | Bhopal | 17,98,218 | 14,37,354 |
| 18 | Visakhapatnam | 17,28,128 | 13,45,938 |
| 19 | Pimpri-Chinchwad | 17,27,692 | 10,12,472 |
| 20 | Patna | 16,84,222 | 13,66,444 |
Most cities show significant population growth from 2001 to 2011. Cities like Bengaluru, Hyderabad, Surat, and Vadodara nearly doubled in population, indicating rapid urbanisation. Mumbai and New Delhi remain the largest cities by a wide margin. Kolkata is the only city whose population slightly decreased.
Suggested title: "Population of India's 20 Largest Cities — A Decade of Growth (2001–2011)"
Pune's population in 2011: 31,15,431 ≈ 31 lakh.
In 2001: 25,38,473 ≈ 25 lakh.
Increase ≈ 31 lakh − 25 lakh = approximately 6 lakh (exact: 5,76,958 ≈ 5.8 lakh).
Absolute increase (approximate):
- Bengaluru: 84 lakh − 43 lakh ≈ 41 lakh increase (largest!)
- Delhi: 110 lakh − 99 lakh ≈ 11 lakh increase
- Hyderabad: 68 lakh − 36 lakh ≈ 32 lakh increase
Bengaluru had the largest absolute increase in population (~41 lakh).
A city's population nearly doubled if 2011 population ≈ 2 × 2001 population:
- Bengaluru: 84 lakh in 2011 vs 43 lakh in 2001 → ratio ≈ 2.0 ✔
- Surat: 45 lakh vs 24 lakh → ratio ≈ 1.85 ✔ (nearly doubled)
- Vadodara: 36 lakh vs 17 lakh → ratio ≈ 2.1 ✔
- Hyderabad: 68 lakh vs 36 lakh → ratio ≈ 1.9 ✔
- Pimpri-Chinchwad: 17 lakh vs 10 lakh → ratio ≈ 1.7 ✔
Patna 2011: ≈ 17 lakh | Mumbai 2011: ≈ 124 lakh
Ratio ≈ 124 ÷ 17 ≈ 7.3
So multiplying Patna's population by approximately 7 gives a number close to Mumbai's population.
Check: 17 × 7 = 119 lakh ≈ 1.19 crore (close to 1.24 crore). ✔
Use the population table to practise estimation and comparison.
- Pick any three cities from the table (ranks 5–20).
- Round each city's 2011 population to the nearest lakh.
- Estimate the total population of your three cities combined. Is it more or less than Mumbai's population?
- Calculate the exact total and compare with your estimate.
- By how many lakhs does the exact total differ from your estimate?
Sample: Ahmedabad + Jaipur + Lucknow
- Ahmedabad: 55,70,585 ≈ 56 lakh
- Jaipur: 30,46,163 ≈ 30 lakh
- Lucknow: 28,15,601 ≈ 28 lakh
- Estimated total: 56 + 30 + 28 = 114 lakh
- Exact total: 55,70,585 + 30,46,163 + 28,15,601 = 1,14,32,349 ≈ 114 lakh
- Difference: Estimate was very close! Mumbai has 1,24,42,373 ≈ 124 lakh. Combined total (114 lakh) is less than Mumbai's population.
Competency-Based Questions — Crores, Estimation & Population
Ten crore = 10,00,00,000; Twenty lakh = 20,00,000; Thirty thousand = 30,000; Forty = 40. Adding: 10,00,00,000 + 20,00,000 + 30,000 + 40 = 10,20,30,040.
(i) 1 million = 10 lakhs (ii) 1 billion = 100 crores (iii) 1 arab = 1 billion
(ii) True. 1 billion = 1,000,000,000 = 1,00,00,00,000 = 100 crores. ✔
(iii) True. 1 arab = 1,00,00,00,000 = 10⁹ = 1 billion. ✔ All three statements are True.
2,34,56,789 → rounded to nearest lakh = 2,35,00,000.
The newspaper reports 2 crore 35 lakh. This is rounding up, since 2,35,00,000 > 2,34,56,789.
(b) Growth factor ≈ 84 ÷ 43 ≈ 2 (nearly doubled in 10 years).
(c) Applying the same factor: 2021 population ≈ 84 lakh × 2 = 168 lakh ≈ 1 crore 68 lakh (actual 2021 estimate is about 1.3 crore, showing growth slowed somewhat).
• Nearest crore = 6 crore: number is between 5,50,00,000 and 6,49,99,999
• Nearest ten lakh = 6,00,00,000: between 5,95,00,000 and 6,04,99,999
• Nearest lakh = 6,00,00,000: between 5,99,50,000 and 6,00,49,999
• Nearest ten thousand = 6,00,00,000: between 5,99,95,000 and 6,00,04,999
• Nearest thousand = 6,00,00,000: between 5,99,99,500 and 6,00,00,499
Intersection: 5,99,99,500 to 6,00,00,499.
Number of whole numbers = 6,00,00,499 − 5,99,99,500 + 1 = 1000 numbers.
Choose the correct option:
(A) Both Assertion and Reason are true; Reason is the correct explanation.
(B) Both true; Reason is NOT the correct explanation.
(C) Assertion is true; Reason is false.
(D) Assertion is false; Reason is true.
Reason (R): In the Indian system, the first grouping from the right has 3 digits (hundreds, tens, ones) and subsequent groupings each have 2 digits (for lakhs, crores, arabs, etc.).
Reason (R): 1 million = 10 lakhs, so 10 million = 100 lakhs = 1 crore.
Reason (R): Rounding down means the approximated number is less than the actual number.
Frequently Asked Questions
What is one crore and how many zeroes does it have?
One crore is 1,00,00,000 which has seven zeroes. It equals 100 lakhs or 10 million in the international system. In the Indian place value system, it occupies the crores place. NCERT Class 7 Ganita Prakash Chapter 1 introduces crore through real-world examples like country populations.
How do you estimate large numbers by rounding?
To estimate a large number, round it to the nearest convenient place value. For numbers in lakhs, round to the nearest lakh. Look at the digit after the rounding place: if it is 5 or more, round up; if less than 5, round down. NCERT Class 7 Chapter 1 teaches estimation with population data.
What is the difference between Indian and international number systems?
The Indian system groups digits as ones-tens-hundreds, then pairs for thousands-lakhs-crores. The international system groups in threes: ones-thousands-millions-billions. One lakh equals 100 thousand and one crore equals 10 million. Both systems are compared in NCERT Class 7 Maths.
How is population data used to teach large numbers?
NCERT Class 7 Ganita Prakash uses India state population data to make large numbers meaningful. Students read, compare and estimate populations in lakhs and crores, learning place value, comma placement and estimation skills through authentic real-world data instead of abstract numbers.
How do you convert between lakhs and crores?
One crore equals 100 lakhs. To convert lakhs to crores, divide by 100. To convert crores to lakhs, multiply by 100. For example, 350 lakhs equals 3.5 crores and 2 crores equals 200 lakhs. This conversion is practised in NCERT Class 7 Ganita Prakash Chapter 1.
Frequently Asked Questions — Large Numbers Around Us
What is Crore, Estimation and Population Data in NCERT Class 7 Mathematics?
Crore, Estimation and Population Data is a key concept covered in NCERT Class 7 Mathematics, Chapter 1: Large Numbers Around Us. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Crore, Estimation and Population Data step by step?
To solve problems on Crore, Estimation and Population Data, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 1: Large Numbers Around Us?
The essential formulas of Chapter 1 (Large Numbers Around Us) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Crore, Estimation and Population Data important for the Class 7 board exam?
Crore, Estimation and Population Data is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Crore, Estimation and Population Data?
Common mistakes in Crore, Estimation and Population Data include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Crore, Estimation and Population Data?
End-of-chapter NCERT exercises for Crore, Estimation and Population Data cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 1, and solve at least one previous-year board paper to consolidate your understanding.