Large Numbers Around Us — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Large Numbers Around Us" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Large Numbers Around Us" — 8 important questions with detailed answers for CBSE boa…
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NCERT Solutions for Class 7 Mathematics — Large Numbers Around Us. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Large Numbers Around Us — All 8 Questions Solved
Q1. Write 45,32,78,901 in words and identify the place value of 7.
Step 1: Break the number into groups of three from right: 901, 32, 45
Step 2: Write in words:
45 crore, 32 lakh, 78 thousand, 901
Or: Forty-five crore, thirty-two lakh, seventy-eight thousand, nine hundred and one
Step 3: Identify place value of 7:
The digit 7 is in the thousands place.
Place value of 7 = 7 × 1000 = 7,000
Answer: Forty-five crore, thirty-two lakh, seventy-eight thousand, nine hundred and one. Place value of 7 is 7,000.
Q2. Round 6,54,789 to the nearest lakh.
Step 1: Identify the digit in the lakh place: 5 (from 6,54,789)
Step 2: Look at the digit to the right (ten-thousands place): 4
Step 3: Apply rounding rule:
Since 4 < 5, round down (keep the lakh digit as 5)
Step 4: Replace all digits to the right with zeros:
6,54,789 ≈ 6,50,000
Answer: 6,50,000
Q3. Estimate: 4,83,627 + 2,15,399
Step 1: Round each number to the nearest lakh:
4,83,627: Look at ten-thousands digit = 8. Since 8 ≥ 5, round up.
4,83,627 ≈ 5,00,000
Step 2: 2,15,399: Look at ten-thousands digit = 1. Since 1 < 5, round down.
2,15,399 ≈ 2,00,000
Step 3: Add the rounded numbers:
5,00,000 + 2,00,000 = 7,00,000
Answer: Estimated sum is 7,00,000 (actual sum: 6,99,026)
Q4. Write 3 × 10⁶ + 2 × 10⁴ + 5 × 10² + 7 in expanded form and standard form.
Step 1: Expand each term:
3 × 10⁶ = 3 × 1,000,000 = 3,000,000
2 × 10⁴ = 2 × 10,000 = 20,000
5 × 10² = 5 × 100 = 500
7 × 10⁰ = 7 × 1 = 7
Step 2: Add all parts:
3,000,000 + 20,000 + 500 + 7 = 3,020,507
Answer: Standard form = 3,020,507; Expanded form = 30,00,000 + 20,000 + 500 + 7
Q5. Compare 78,54,321 and 87,45,123. Which is greater?
Step 1: Compare the leftmost digits (crores place):
78,54,321 has 7 in crores place
87,45,123 has 8 in crores place
Step 2: Since 8 > 7, we know 87,45,123 > 78,54,321
Answer: 87,45,123 is greater than 78,54,321
Q6. The population of India is approximately 1,417,173,173. Write this in words using the Indian place value system.
Step 1: Break into groups of two from right: 73, 71, 71, 41, 1
Step 2: Identify positions:
73 (ones and tens)
71 (hundreds and thousands)
71 (ten-thousands and lakhs)
41 (millions and crores) — wait, recalculate
Actually: 1,41,71,73,173
Breakdown: 1 crore 41 million (or: 1 Arab 41 crore 71 lakh 73 thousand 173)
Step 3: In standard Indian system:
1 billion = 1 Arab or 100 crore
So: 1 Arab, 41 crore, 71 lakh, 73 thousand, 173
Or: One billion four hundred seventeen million one hundred seventy-three thousand one hundred seventy-three
Answer: One Arab, forty-one crore, seventy-one lakh, seventy-three thousand, one hundred seventy-three
Q7. A school spent 95,42,500 on infrastructure. Estimate to the nearest crore.
Step 1: Identify the digit in the crores place: 9
Step 2: Look at the digit to the right (ten-lakhs place): 5
Step 3: Apply rounding rule:
Since 5 ≥ 5, round up (increase the crore digit from 9 to 10)
Step 4: 95,42,500 ≈ 1,00,00,000
Answer: Estimated amount is 1 crore or 1,00,00,000
Q8. Write the number that comes just before 1,00,00,000 (1 crore).
Step 1: To find the number just before 1,00,00,000, subtract 1:
1,00,00,000 - 1 = 99,99,999
Step 2: Verify:
99,99,999 + 1 = 1,00,00,000 ✓
Answer: 99,99,999
Large Numbers Around Us — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. What is the place value of the digit '5' in the number 7,53,42,189 according to the Indian Place Value System?
- A. Lakhs
- B. Ten Lakhs
- C. Crores
- D. Ten Crores
Answer: B. Ten Lakhs — In the Indian system, the place values are Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, Ten Crores. The digit '5' is in the Ten Lakhs place.
MCQ 2. What is the place value of the digit '7' in the number 876,543,210 according to the International Place Value System?
- A. Ten Million
- B. Hundred Million
- C. Million
- D. Billion
Answer: A. Ten Million — In the International system, the place values are Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, Hundred Millions. The digit '7' is in the Ten Millions place.
MCQ 3. How is the number 'Fifty-six lakh forty-two thousand one hundred seventy-three' written in figures according to the Indian system?
- A. 56,42,173
- B. 5,642,173
- C. 56,421,73
- D. 564,217,3
Answer: A. 56,42,173 — In the Indian system, commas are placed after the hundreds place (three digits from the right), then after every two digits. Fifty-six lakh is 56,00,000, forty-two thousand is 42,000, and one hundred seventy-three is 173.
MCQ 4. How is the number 'Two hundred forty-five million three hundred sixty thousand eight hundred nine' written in figures according to the International system?
- A. 24,53,60,809
- B. 245,360,809
- C. 245,36,0809
- D. 2,453,608,09
Answer: B. 245,360,809 — In the International system, commas are placed after every three digits from the right. Two hundred forty-five million is 245,000,000, three hundred sixty thousand is 360,000, and eight hundred nine is 809.
MCQ 5. Which of the following numbers is the largest?
- A. 98,76,543
- B. 9,87,65,432
- C. 98,76,534
- D. 9,87,65,342
Answer: B. 9,87,65,432 — To compare numbers, first compare the number of digits. The numbers with 8 digits (9,87,65,432 and 9,87,65,342) are larger than numbers with 7 digits. Comparing the 8-digit numbers, 9,87,65,432 is greater than 9,87,65,342.
MCQ 6. Arrange the following numbers in ascending order: 12,34,567; 1,23,45,678; 12,34,657; 1,23,45,670.
- A. 1,23,45,670; 1,23,45,678; 12,34,567; 12,34,657
- B. 12,34,567; 12,34,657; 1,23,45,670; 1,23,45,678
- C. 12,34,657; 12,34,567; 1,23,45,678; 1,23,45,670
- D. 1,23,45,678; 1,23,45,670; 12,34,657; 12,34,567
Answer: B. 12,34,567; 12,34,657; 1,23,45,670; 1,23,45,678 — First, group by the number of digits. 12,34,567 and 12,34,657 are 7-digit numbers. 1,23,45,678 and 1,23,45,670 are 8-digit numbers. Comparing 7-digit numbers: 12,34,567 < 12,34,657. Comparing 8-digit numbers: 1,23,45,670 < 1,23,45,678. So the ascending order is 12,34,567; 12,34,657; 1,23,45,670; 1,23,45,678.
MCQ 7. What is the smallest 6-digit number that can be formed using the digits 3, 0, 7, 1, 5, 9, each only once?
- A. 013579
- B. 103579
- C. 130579
- D. 103759
Answer: B. 103579 — To form the smallest number, arrange the digits in ascending order. Since a 6-digit number cannot start with 0, place the smallest non-zero digit (1) at the beginning, followed by 0, then the remaining digits in ascending order.
MCQ 8. What is the largest 7-digit number that can be formed using the digits 8, 2, 0, 5, 9, 1, 4, each only once?
- A. 9854210
- B. 9854201
- C. 9854120
- D. 9852410
Answer: A. 9854210 — To form the largest number, arrange the digits in descending order from left to right. The digits are 9, 8, 5, 4, 2, 1, 0.
MCQ 9. Round off 3,45,678 to the nearest hundred.
- A. 3,45,600
- B. 3,45,700
- C. 3,46,000
- D. 3,45,680
Answer: B. 3,45,700 — To round to the nearest hundred, look at the tens digit. If it is 5 or greater, round up the hundreds digit. Here, the tens digit is 7, so we round up 6 to 7.
MCQ 10. Round off 12,34,567 to the nearest lakh.
- A. 12,00,000
- B. 13,00,000
- C. 12,30,000
- D. 12,40,000
Answer: A. 12,00,000 — To round to the nearest lakh, look at the ten thousands digit. If it is less than 5, round down. Here, the ten thousands digit is 3, which is less than 5, so we keep the lakhs digit as 2 and replace the remaining digits with zeros.
MCQ 11. Estimate the sum of 87,654 and 34,210 by rounding off each number to the nearest thousand.
- A. 1,21,000
- B. 1,22,000
- C. 1,20,000
- D. 1,23,000
Answer: B. 1,22,000 — Rounding 87,654 to the nearest thousand gives 88,000 (since hundreds digit is 6). Rounding 34,210 to the nearest thousand gives 34,000 (since hundreds digit is 2). The estimated sum is 88,000 + 34,000 = 1,22,000.
MCQ 12. Estimate the difference between 7,89,123 and 3,45,678 by rounding off each number to the nearest ten thousand.
- A. 4,40,000
- B. 4,50,000
- C. 4,30,000
- D. 4,60,000
Answer: A. 4,40,000 — Rounding 7,89,123 to the nearest ten thousand gives 7,90,000 (since thousands digit is 9). Rounding 3,45,678 to the nearest ten thousand gives 3,50,000 (since thousands digit is 5). The estimated difference is 7,90,000 - 3,50,000 = 4,40,000.
MCQ 13. What is the Roman numeral for 99?
- A. XCIX
- B. IC
- C. LXXXXIX
- D. CXI
Answer: A. XCIX — 99 can be written as 100 - 10 + 9. In Roman numerals, 90 is XC and 9 is IX. Thus, 99 is XCIX.
MCQ 14. What is the Hindu-Arabic numeral for the Roman numeral 'MCMXLV'?
- A. 1945
- B. 1965
- C. 1845
- D. 1955
Answer: A. 1945 — M = 1000, CM = 900 (1000-100), XL = 40 (50-10), V = 5. So, 1000 + 900 + 40 + 5 = 1945.
MCQ 15. How many millimetres (mm) are there in 5 metres (m)?
- A. 500 mm
- B. 5,000 mm
- C. 50,000 mm
- D. 50 mm
Answer: B. 5,000 mm — 1 metre = 100 centimetres, and 1 centimetre = 10 millimetres. Therefore, 1 metre = 100 × 10 = 1,000 millimetres. So, 5 metres = 5 × 1,000 = 5,000 millimetres.
MCQ 16. A bag contains 25 kg of rice. How many grams of rice are there in the bag?
- A. 250 g
- B. 2,500 g
- C. 25,000 g
- D. 2,50,000 g
Answer: C. 25,000 g — 1 kilogram (kg) is equal to 1,000 grams (g). Therefore, 25 kg = 25 × 1,000 g = 25,000 g.
MCQ 17. A milk dairy produces 5,500 litres of milk per day. If it supplies 2,350 litres to shops and 1,875 litres to restaurants, how much milk is left with the dairy?
- A. 1,275 litres
- B. 1,225 litres
- C. 1,325 litres
- D. 1,375 litres
Answer: A. 1,275 litres — Total milk supplied = 2,350 litres (shops) + 1,875 litres (restaurants) = 4,225 litres. Milk left = Total production - Total supplied = 5,500 litres - 4,225 litres = 1,275 litres.
MCQ 18. A person earns ₹75,000 per month. If he spends ₹48,500 on household expenses and ₹12,800 on other expenses, how much does he save in a month?
- A. ₹13,700
- B. ₹13,500
- C. ₹12,700
- D. ₹13,200
Answer: A. ₹13,700 — Total expenses = ₹48,500 + ₹12,800 = ₹61,300. Savings = Total earnings - Total expenses = ₹75,000 - ₹61,300 = ₹13,700.
MCQ 19. What is the difference between the place value and face value of the digit '6' in the number 46,789?
- A. 5,994
- B. 6,000
- C. 6
- D. 5,996
Answer: D. 5,996 — The place value of 6 in 46,789 is 6,000 (thousands place). The face value of 6 is 6. The difference is 6,000 - 6 = 5,994.
MCQ 20. What is the greatest 4-digit number that can be formed using the digits 3, 0, 8, 3?
- A. 8330
- B. 8303
- C. 3830
- D. 8033
Answer: A. 8330 — To form the greatest number using the given digits 3, 0, 8, 3, arrange them in descending order. This gives 8330.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.