NCERT Solutions for Class 12 Mathematics Ganita Prakash Chapter 1
NCERT solutions for Class 7 Mathematics Ganita Prakash Chapter 1: Large Numbers – complete answers & explanations
This blog provides NCERT solutions for Class 7 Mathematics Chapter 1 Large Numbers. In this chapter, students learn about large numbers, place value systems, number patterns, and real-life applications of numbers. It is an important chapter as it builds a strong foundation for understanding numbers used in daily life and higher classes. These solutions are created strictly based on the worksheet :contentReference[oaicite:0]{index=0} and include all answers in the exact format for easy learning and revision.
What this NCERT chapter covers?
1. Understanding large numbers and place
value systems
2. Reading and writing numbers in Indian and International systems
3. Comparing and estimating large numbers
4. Using multiplication and division in real-life contexts
5. Understanding patterns and number relationships
6. Applying concepts through activities and problem-solving
How to use these NCERT solutions?
1. First, try solving all questions from the worksheet on your own
2. Use these answers only to check your work and correct mistakes
3. Focus on understanding steps rather than memorizing answers
4. Parents and teachers can guide students using these solutions
5. Follow the exact order of questions as given in the worksheet
Important tips & tricks for students
1. Always write numbers correctly using place value commas
2. Double-check calculations in multiplication and division
3. Read questions carefully before solving
4. Practice estimation questions to improve accuracy
5. Attempt activity-based questions thoughtfully
NCERT solutions – complete answer key
But how much is one lakh? Observe the pattern and fill in the boxes given below.
The smallest 4-digit number: 1,000
The largest 4-digit number: 9,999
The smallest 5-digit number: 10,000
The largest 5-digit number: 99,999
Explanation: This question helps students understand how numbers increase when we move from 3-digit to 6-digit numbers. The smallest number of the next place value is always 1 more than the largest number of the previous place value.
Number pattern near one lakh:
99,995
99,996
99,997
99,998
99,999
1,00,000
1,00,001
1,00,002
1,00,003
1,00,004
Figure it Out
25,000
6,000
31,000
Explanation: In this section, we compare numbers with one lakh and understand differences between numbers. We also estimate heights using the picture where Somu’s height helps approximate the building height.
Getting a Feel of Large Numbers
Approximate building height: 40 m
Statue of Unity is taller by: 140 m
Kunchikal waterfall is taller than the building by: 410 m
Number of floors required: 113 floors (approx.)
Explanation: In this section, we compare numbers with one lakh and understand differences between numbers. We also estimate heights using the picture where Somu’s height helps approximate the building height.
Reading and Writing Numbers
Three lakh six hundred
Twenty seven lakh thirty thousand
Seventy lakh fifty three thousand one hundred thirty eight
Five lakh four thousand eighty five
Explanation: Here we convert numbers written in digits into words using the Indian place value system.
Write the corresponding number in the Indian place value system for each of the following:
1,23,456
4,07,704
50,05,050
10,00,235
Explanation: In this exercise, we convert number names into numbers using the Indian place value system.
1.2 Land of Tens
3 times
10 times
53 times
90 times
Explanation: These questions help us understand how large numbers are built using thousands, tens, and hundreds. Each calculator button adds a fixed value repeatedly.
Thoughtful Thousands
1,53,000
100
100 times
Tedious Tens
50 times
78 times
100 times
370 times
Handy Hundreds
4 times
37 times
100 times
530 times
900 times
976 times
1000 times
58,200
100
1000
No
Find a different way to get 5072 and write an expression for the same.
(5 × 1000) + (7 × 10) + (2 × 1) = 5072
Explanation: Different combinations of button presses can produce the same number. This question asks for another expression for 5072.
Figure it Out
1. For each number given below, write expressions for at least two different ways to obtain the number through button clicks.
(8 × 1000) + (3 × 100)
or, (5 × 1000) + (33 × 100)
(56 × 1000) + (3 × 100) + (5 × 10) + (4 × 1)
or, (46 × 1000) + (103 × 100) + (54 × 1)
(66 × 1000) + (6 × 100) + (66 × 1)
or, (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1)
(40 × 1000) + (6 × 100) + (2 × 10) + (9 × 1)
or, (30 × 1000) + (106 × 100) +(29 × 1)
(3 × 100000) + (6 × 10000) + (7 × 1000) ) + (8 × 100) + (1 × 10) + (3 × 1)
or, (36 × 10000) + (78 × 1000) + (13 × 1)
Creative Chitti has some questions for you —
A. Explanation: You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make?
993 is the largest 3-digit number that can be made using 30 button presses.
102 is the smallest 3-digit number that can be made using 30 button presses.
B. Explanation: 997 can be made using 25 clicks. Can you make 997 with a different number of clicks?
997 can also be made as –
(8 × 100) + (19 × 10) + (7 × 1)
Number of clicks = 8 + 19 + 7
= 34
How can we get the numbers (a) 5072, (b) 8300, using as few button clicks as possible?
5072 = (5 × 1000) + (7 × 10) + (2 × 1)
Number of clicks = 1
8300 = (8 × 1000) + (3 × 100)
Number of clicks = 11
Figure it Out
1. For the numbers in the previous exercise, find out how to get each number by making the smallest number of button clicks and write the expression.
8300 = (8 × 1000) + (3 × 100)
Number of clicks = 11
(5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1)
Number of clicks = 5 + 6 + 3 + 5 + 4 = 23
(6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1)
Number of clicks = 6 + 6 + 6 + 6 + 6 = 30
(4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1)
Number of clicks = 4 + 6 + 2 + 9 = 21
(3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 1)
Number of clicks = 3 + 6 + 7 + 8 + 1 + 3 = 28
2. Do you see any connection between each number and the corresponding smallest number of button clicks?
The smallest number of buttons click for each number is the sum of its digit.
How many zeros does a thousand lakh have?
8 zeros
How many zeros does a hundred thousand have?
5 zeros
Figure it Out
1. Read the numbers and write their number names in both the Indian and American systems:
4050678
Indian System: Forty Lakh Fifty Thousand Six Hundred Seventy-Eight
American System: Four Millions Fifty Thousand Six Hundred Seventy-Eight
48121620
Indian System: Four Crore Eighty-One Lakh Twenty-One Thousand Six Hundred Twenty
American System: Forty Eight Millions One Hundred Twenty One Thousand Six Hundred Twenty
20022002
Indian System: Two Crore Twenty Two Thousand Two
American System: Twenty millions twenty two thousand and two
246813579
Indian System: Twenty Four Crore Sixty Eight Lakh Thirteen Thousand Five Hundred Seventy Nine
American System: Two Hundred Forty Six Millions Eight Hundred Thirteen Thousand Five Hundred Seventy Nine
345000543
Indian System: Thirty four crore fifty lakh five hundred forty three
American System: Three hundred forty five millions five hundred forty three
1020304050
Indian System: One Arab two crore three lakh four thousand fifty
American System: One billion twenty millions three hundred four thousand fifty
2. Write the following numbers in Indian place value notation:
1,01,01,010
10,20,30,040
9,08,07,00,600
1,00,10,01,001
3. Compare and write ‘<’, ‘>’ or ‘=’
30 thousand < 3 lakhs
800 thousand < 8 million
640 crore < 60 billion
500 lakhs > 5 million
Think and share situations where it is appropriate to (a) round up, (b) round down, (c) either rounding up or rounding down is okay and (d) when exact numbers are needed.
(a) Buying food/fruits for a group.
(b) Estimating time remaining to leave for the school (catching the school bus).
(c) Distance estimation between places, especially far off places.
(d) Handling money in banks.
Similarly, write the five nearest neighbours for these numbers:
3,87,69,957
Nearest thousand 3,87,70,000
Nearest ten thousand 3,87,70,000
Nearest lakh 3,88,00,000
Nearest ten lakh 3,90,00,000
Nearest crore 4,00,00,000
29,05,32,481
Nearest thousand 29,05,32,000
Nearest ten thousand 29,05,30,000
Nearest lakh 29,05,00,000
Nearest ten lakh 29,10,00,000
Nearest crore 29,00,00,000
From the information given in the table answer the following questions by approximation:
One of the observations is –
Most cities shown in the table have seen a significant rise in population from 2001 to 2011.
Population of Pune in 2011 is 31,15,431.
The population of Pune has approximately increased by 6 lakh.
Bengaluru has shown maximum increase in population which is 41,24,644.
Yes, they are Bengaluru, Hyderabad, Surat and Vadodara
We need to multiply Patna’s population by 7.39 to get a number close to the population of Mumbai.
Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10?
10 ÷ 2 is the same as 5.
1. Find quick ways to calculate these products:
2*1768*50
= 2*50*1768
= 100*1768
72 × 125
= 72 × 1000
8
= 72
8
× 1000 = 9 × 1000
125*40*8*25
= 125*8*40*25
= 1000*1000
2. Calculate these products quickly.
25 × 12
= 100
4
× 12
= 100 × 12
4
= 100 × 3
25 × 240
= 100 × 60
250 × 120
= 1000 × 30
= 10,000 × 3
1200 × 1,00,000 = 120000000
Observe the number of digits in the two numbers being multiplied and their product in each case.
The maximum digits in their product will be the sum of the digits of the two numbers. The minimum digit in their product will be one less than their sum.
Roxie says that the product of two 2-digit numbers can only be a 3- or a 4-digit number. Is she correct?
Yes, Roxie is correct.
Should we try all possible multiplications with 2-digit numbers to tell whether Roxie’s claim is true? Or is there a better way to find out?
She can just check the minimum and maximum number of digits possible.
Can multiplying a 3-digit number with another 3-digit number give a 4-digit number?
No.
Can multiplying a 4-digit number with a 2-digit number give a 5-digit number?
Yes.
Find out if you can reach the Sun in a lifetime, if you travel 1000 kilometers every day.
We cannot reach the sun in a lifetime because it takes approx. 403 years.
Make necessary reasonable assumptions and answer the questions below:
(a) Weight of one lakh (1,00,000) sheets = 500 kg.
Since a person cannot lift 500 kg so, we cannot lift one lakh sheets of paper.
(b) Babies born in one day = 3,60,000 babies.
3,60,000 is less than one million (10 lakh)
Hence, a million babies cannot born in a day.
(c) No. Because, Coins counted per day = 86,400
1. Largest multiple of 5 = 9876543210
2. One such number is 77,77,777, which has 60 letters.
3. One such number is 987654312.
4. 5534512345
6. (a) The first digit of 370, which is 3, is the 1000th digit.
(b) The millionth digit occurs in the number 185184+1=1,85,185.
(c) 13995
7.
20,800 = (2 × 10,000) + (8 × 100)
Total clicks = 2 + 8 = 10 button clicks.
92,100 = (9 × 10,000) + (21 × 100)
Total clicks = 9 + 21 = 30 button clicks.
1,20,500 = (12 × 10,000) + (5 × 100)
Total clicks = 12 + 5 = 17 button clicks.
65,30,000 = (653 × 10,000)
Total clicks = 653 button clicks.
70,25,700 = (702 × 10,000) + (57 × 100)
Total clicks = 759 button clicks.
8. 10,000 lakh make a billion.
9.
Sum = 1,00,54,320
Difference = 10,22,447
10.
1,10,000: 4000 * (20 + 5) + 13000 = 1,13,000
closest estimate = 1,50,000 + 70,000 – (4000 × 5) = 2,00,000.
closest estimate = (1,50,000 × 4) – (4000 × 5) = 5,80,000.
closest estimate = (70,000 × 20) – 1,50,000 – 4,000 – (300 × 5) = 12,44,500.
closest estimate = (1,50,000 × 14) + 4,000 – 13,000 = 20,91,000.
11.
Number of coins to be stacked = 1,80,000 coins.
12.
Estimated number of days if it flies 900 km/day = 13.3 days
Estimated number of days if it flies 1000 km/day = 12 days
13.
Distance covered per day = 1232.73 km or 1233 km
Distance covered per hour = 51.36 km or 51 km
14.
Bald eagles fly about 112 to 150 times higher than Somu’s building.
Mount Everest is approximately 221 times taller than Somu’s building.
Airplanes fly about 250 to 320 times as high as Somu’s building.
Why NCERT solutions help students?
NCERT solutions help students understand concepts clearly and prepare effectively for exams. They ensure answers are accurate, structured, and aligned with NCERT guidelines. Using these solutions regularly builds confidence and improves problem-solving skills.
Help your child build strong Mathematics fundamentals with expert-guided learning support.