This MCQ module is based on: Large Numbers: Lakh and Place Value
TOPIC 1 OF 31
Large Numbers: Lakh and Place Value
🎓 Class 7
Mathematics
CBSE
Theory
Ch 1 — Large Numbers Around Us
⏱ ~30 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Large Numbers: Lakh and Place Value
Targeting Class 7 level in Number Theory, with Basic difficulty.
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1.1 A Lakh Varieties!
India once had about a lakh? varieties of rice! But how much is one lakh? Let us build up to it step by step.
📖 Building Up to a Lakh
| The largest 3-digit number is | 999 |
| The smallest 4-digit number is | 1,000 |
| The largest 4-digit number is | 9,999 |
| The smallest 5-digit number is | 10,000 |
| The largest 5-digit number is | 99,999 |
| The smallest 6-digit number is | 1,00,000 = One Lakh |
⚠️ Key Fact
1 Lakh = 1,00,000 — It is 1 followed by 5 zeroes. It equals 100 thousands, or 10 ten-thousands.
Is One Lakh Big or Small?
It depends on what you are counting!
1 Lakh is BIG
1 lakh varieties of rice is a lot! Living 1 lakh days = 274 years — a really long time.
1 Lakh is SMALL
1 lakh rupees cannot buy a house. The distance to the Moon is 38 lakh km — 1 lakh km barely covers 1/38th.
💡 Did You Know?
The number of seconds in a day is 86,400 — that is close to a lakh! So you breathe roughly a lakh times every day (about 15 breaths per minute × 1440 minutes ≈ 21,600 — but including sleep, some estimates go higher).
Figure it Out (Page 3)
Q1. The population of Chintamani was about 75,000 (2011 Census). How much less than one lakh is 75,000?
Answer: \(1{,}00{,}000 - 75{,}000 = \mathbf{25{,}000}\). So 75,000 is 25,000 less than one lakh.
Q2. The estimated population of Chintamani in 2024 is 1,06,000. How much more than one lakh is this?
Answer: \(1{,}06{,}000 - 1{,}00{,}000 = \mathbf{6{,}000}\). The population is 6,000 more than one lakh.
Q3. Choose a number for y. How close to one lakh is the number of days in y years?
Answer: 1 year ≈ 365 days. For y = 274 years: \(274 \times 365 = 1{,}00{,}010\) — very close to 1 lakh!
For y = 100 years: \(100 \times 365 = 36{,}500\) — only about a third of a lakh.
So it takes about 274 years to live 1 lakh days.
For y = 100 years: \(100 \times 365 = 36{,}500\) — only about a third of a lakh.
So it takes about 274 years to live 1 lakh days.
1.2 Indian Place Value System
In the Indian place value system?, commas are placed after the first 3 digits from the right, and then after every 2 digits. The place values are: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs.
Indian Place Value Chart — 1,23,456
Lakhs
1
Ten Thousands
2
Thousands
3
Hundreds
4
Tens
5
Ones
6
One lakh twenty-three thousand four hundred and fifty-six
Writing Numbers in Words
Write the corresponding number for: (a) One lakh twenty-three thousand four hundred and fifty-six (b) Four lakh seven thousand seven hundred and four (c) Fifty lakhs five thousand and fifty
Answer:
(a) 1,23,456
(b) 4,07,704
(c) 50,05,050
(a) 1,23,456
(b) 4,07,704
(c) 50,05,050
Write in words: (a) 7,34,555 (b) 11,11,111 (c) 27,30,000 (d) 70,53,138
Answer:
(a) Seven lakh thirty-four thousand five hundred and fifty-five
(b) Eleven lakh eleven thousand one hundred and eleven
(c) Twenty-seven lakh thirty thousand
(d) Seventy lakh fifty-three thousand one hundred and thirty-eight
(a) Seven lakh thirty-four thousand five hundred and fifty-five
(b) Eleven lakh eleven thousand one hundred and eleven
(c) Twenty-seven lakh thirty thousand
(d) Seventy lakh fifty-three thousand one hundred and thirty-eight
Handy Hundreds
How many hundreds make up larger numbers? Dividing by 100 tells us!
How many hundreds are in: (a) 400 (b) 3,700 (c) 10,000 (d) 53,000 (e) 90,000 (f) 97,600 (g) 1,00,000
Answer:
(a) 400 = 4 hundreds
(b) 3,700 = 37 hundreds
(c) 10,000 = 100 hundreds
(d) 53,000 = 530 hundreds
(e) 90,000 = 900 hundreds
(f) 97,600 = 976 hundreds
(g) 1,00,000 = 1,000 hundreds
So 1 lakh = 1,000 hundreds!
(a) 400 = 4 hundreds
(b) 3,700 = 37 hundreds
(c) 10,000 = 100 hundreds
(d) 53,000 = 530 hundreds
(e) 90,000 = 900 hundreds
(f) 97,600 = 976 hundreds
(g) 1,00,000 = 1,000 hundreds
So 1 lakh = 1,000 hundreds!
Button Click Number Machine
Bloom: L3 ApplyClick the buttons to build numbers. How can you make 8300? Try with fewest clicks!
0
Clicks: 0
In words: Zero
Figure it Out — Button Clicks (Pages 6–7)
Q1. Write expressions for at least two different ways to get 8300 through button clicks.
Answer:
Way 1: \(8 \times 1000 + 3 \times 100\) → 11 clicks
Way 2: \(5 \times 1000 + 33 \times 100\) → 38 clicks
Way 3: \(83 \times 100\) → 83 clicks
The fewest clicks = sum of digits = 8 + 3 = 11 clicks.
Way 1: \(8 \times 1000 + 3 \times 100\) → 11 clicks
Way 2: \(5 \times 1000 + 33 \times 100\) → 38 clicks
Way 3: \(83 \times 100\) → 83 clicks
The fewest clicks = sum of digits = 8 + 3 = 11 clicks.
Q2. You must make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest?
Answer:
Largest: Use as many +100 clicks as possible. \(30 \times 100 = 3000\) — but that is 4 digits! So use 9 clicks of +100 + remaining 21 clicks of +10 + remaining 0 of +1... We need digit sum = 30 and result ≤ 999. Try: \(9 \times 100 + 9 \times 10 + 12 \times 1 = 900 + 90 + 12 = 1002\) — too much! Adjust: \(9 \times 100 + 9 \times 10 + 3 \times 1 = 993\) uses 21 clicks. To use 30: \(9 \times 100 + 2 \times 10 + 1 \times 1 = 921\) uses 12 clicks... This needs creative thinking!
Smallest 3-digit: \(1 \times 100 + 0 \times 10 + 29 \times 1 = 129\) uses 30 clicks.
Largest: Use as many +100 clicks as possible. \(30 \times 100 = 3000\) — but that is 4 digits! So use 9 clicks of +100 + remaining 21 clicks of +10 + remaining 0 of +1... We need digit sum = 30 and result ≤ 999. Try: \(9 \times 100 + 9 \times 10 + 12 \times 1 = 900 + 90 + 12 = 1002\) — too much! Adjust: \(9 \times 100 + 9 \times 10 + 3 \times 1 = 993\) uses 21 clicks. To use 30: \(9 \times 100 + 2 \times 10 + 1 \times 1 = 921\) uses 12 clicks... This needs creative thinking!
Smallest 3-digit: \(1 \times 100 + 0 \times 10 + 29 \times 1 = 129\) uses 30 clicks.
💡 Key Insight
The smallest number of button clicks to make any number equals the sum of its digits. For example, 8300 has digits 8+3+0+0 = 11, so the minimum clicks = 11.
🔍 Activity 1.1 — How Big is a Lakh?
Bloom: L3 Apply
Materials needed: Notebook, calculator (optional)
🤔 PREDICT FIRST: Guess: How many seconds are there in one day? Is it more or less than a lakh?
- Calculate the number of seconds in 1 day: \(60 \times 60 \times 24 = ?\)
- Is it more or less than 1 lakh (1,00,000)?
- How many days would it take to count to 1 lakh if you count one number per second?
- How many hours is that? How many whole days?
✅ Observation & Explanation
Seconds in 1 day = \(60 \times 60 \times 24 = 86{,}400\) — less than 1 lakh!To count to 1 lakh at 1 per second: \(\frac{1{,}00{,}000}{86{,}400} \approx 1.16\) days ≈ about 27 hours 47 minutes.
So counting non-stop, it would take more than a full day to reach 1 lakh!
📋
Competency-Based Questions
Scenario: A school is organising a book fair. They received 2,45,000 books from different publishers and need to arrange them in the library. The library has 500 shelves, each holding 100 books.
Q1. How many lakhs of books did the school receive?
L2 Understand
Answer: (B) 2.45 lakhs — \(2{,}45{,}000 = 2\) lakhs \(45\) thousand = \(2.45\) lakhs.
Q2. Can all the books fit on the library shelves? How many more shelves are needed?
L3 Apply
Answer: Current capacity = \(500 \times 100 = 50{,}000\) books. Books received = 2,45,000.
Shortfall = \(2{,}45{,}000 - 50{,}000 = 1{,}95{,}000\) books.
Additional shelves needed = \(\frac{1{,}95{,}000}{100} = \mathbf{1{,}950}\) more shelves.
Shortfall = \(2{,}45{,}000 - 50{,}000 = 1{,}95{,}000\) books.
Additional shelves needed = \(\frac{1{,}95{,}000}{100} = \mathbf{1{,}950}\) more shelves.
Q3. "2,45,000 is roughly 2.5 lakhs." Is this a good estimation? When would exact vs. estimated numbers be more appropriate?
L5 Evaluate
Model Answer: Yes, 2.5 lakhs is a good estimate (error = only 5,000 or 2%). Estimation is useful for quick planning, news reports, and general discussions. Exact numbers are needed for accounting, billing, and ordering specific quantities (e.g., ordering exactly 1,950 shelves, not "about 2,000").
HOT Q. Create a real-life situation where the difference between "about 1 lakh" and the exact number matters significantly.
L6 Create
Hint: Think of situations involving money (salary, loan repayment), medicine (doses), or elections (vote counts). For example: "A candidate won by 99,990 votes vs. 1,00,010 votes — the difference of 20 votes could change the result, so 'about 1 lakh each' would miss the winner!"
⚖️ Assertion–Reason Questions
Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is NOT the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is NOT the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.
Assertion (A): 1 lakh = 1,000 hundreds.
Reason (R): \(1{,}00{,}000 \div 100 = 1{,}000\).
Answer: (A) — Both true. Dividing 1 lakh by 100 gives 1,000, confirming that 1 lakh contains exactly 1,000 hundreds. R correctly explains A.
Assertion (A): The minimum number of button clicks to make 5070 is 12.
Reason (R): The minimum clicks equals the sum of the digits of the number.
Answer: (A) — Both true. Digits of 5070: 5+0+7+0 = 12. R correctly explains the pattern: using the largest button values minimises clicks, and this equals the digit sum.
Frequently Asked Questions
What is one lakh in the Indian number system?
One lakh equals 1,00,000 which is one followed by five zeroes. It is the smallest six-digit number in the Indian number system. In the Indian comma notation, commas are placed after every two digits from the right after the hundreds place, giving 1,00,000. This is taught in NCERT Class 7 Ganita Prakash Chapter 1.
How does the Indian place value system work?
The Indian place value system groups digits as ones, tens, hundreds, then thousands and ten-thousands, then lakhs and ten-lakhs, then crores. Commas separate these groups. Each position is ten times the one before it. NCERT Class 7 Maths Chapter 1 explains this system with place value charts.
How do you write a number in expanded form?
To write a number in expanded form, express each digit multiplied by its place value and add them together. For example, 3,52,461 equals 3 lakhs plus 5 ten-thousands plus 2 thousands plus 4 hundreds plus 6 tens plus 1. This skill is practised in NCERT Class 7 Chapter 1.
How do you compare large numbers?
To compare large numbers, first check which has more digits because more digits means a larger number. If both have the same number of digits, compare digits from left to right and the first position where digits differ determines which number is larger. NCERT Class 7 Maths Chapter 1 covers this topic.
Is one lakh big or small?
Whether one lakh is big or small depends on context. One lakh varieties of rice is impressive, and living one lakh days would mean 274 years. But one lakh rupees cannot buy a house, and the Moon is 38 lakh kilometres away. NCERT Class 7 Ganita Prakash uses such examples to build number sense.
Frequently Asked Questions — Large Numbers Around Us
What is Large Numbers: Lakh and Place Value in NCERT Class 7 Mathematics?
Large Numbers: Lakh and Place Value 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 Large Numbers: Lakh and Place Value step by step?
To solve problems on Large Numbers: Lakh and Place Value, 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 Large Numbers: Lakh and Place Value important for the Class 7 board exam?
Large Numbers: Lakh and Place Value 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 Large Numbers: Lakh and Place Value?
Common mistakes in Large Numbers: Lakh and Place Value 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 Large Numbers: Lakh and Place Value?
End-of-chapter NCERT exercises for Large Numbers: Lakh and Place Value 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.
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