Get Class 7 Maths Chapter 1 solutions and easy explanations for Large Numbers Around Us. Learn lakhs, crores, millions, number systems, estimation, rounding and number patterns with step-by-step examples and original practice questions.
Class 7 Maths Chapter 1, Large Numbers Around Us, introduces students to numbers much larger than the quantities they normally use in everyday calculations. The chapter develops an understanding of lakhs and crores along with the million and billion system used internationally.
The current NCERT Mathematics textbook for Grade 7 is Ganita Prakash, Part I. NCERT’s official 2026–27 reprint identifies Large Numbers Around Us as Chapter 1 and describes the chapter as an introduction to lakhs, crores, millions and billions through practical situations and exploration.
This chapter is not only about reading large numbers. It also develops skills such as:
The aim of this page is to explain these ideas in simple language so that a Class 7 student can understand the method instead of simply memorising answers.
| Particular | Details |
|---|---|
| Class | 7 |
| Subject | Mathematics |
| Book | Ganita Prakash, Part I |
| Chapter | 1 |
| Chapter Name | Large Numbers Around Us |
| Main Topic | Large numbers and their applications |
| Academic reference | 2026–27 |
| Level | Class 7 |
The official NCERT textbook is a 2026–27 reprint of the Grade 7 Ganita Prakash Part I textbook.
We see large numbers in many real-life situations.
For example:
A number such as 75 is easy to imagine.
But numbers such as:
75,00,00075,00,000
or
7,50,00,0007,50,00,000
require a better understanding of place value.
This chapter helps students become comfortable with such numbers.
The value of a digit depends on its position in a number.
Consider:
4,58,23,6174,58,23,617
Using the Indian number system, we can separate it as:
Therefore:
4,58,23,6174,58,23,617
is read as:
Four crore fifty-eight lakh twenty-three thousand six hundred seventeen.
The important point is that commas help us recognise groups of digits, but the actual value comes from place value.
In the Indian system, commas are generally placed after the first three digits from the right and then after every two digits.
For example:
123456789123456789
is written as:
12,34,56,78912,34,56,789
The groups are:
| Group | Value |
|---|---|
| Crore | 12 |
| Lakh | 34 |
| Thousand | 56 |
| Ones group | 789 |
So the number is:
12 crore 34 lakh 56 thousand 789.
| Number | Name |
|---|---|
| 1,000 | One thousand |
| 10,000 | Ten thousand |
| 1,00,000 | One lakh |
| 10,00,000 | Ten lakh |
| 1,00,00,000 | One crore |
| 10,00,00,000 | Ten crore |
| 1,00,00,00,000 | One arab |
Students should pay particular attention to the difference between lakh and crore.
Let us consider:
6,42,15,3086,42,15,308
Separate the number according to the Indian system:
Therefore, it is read as:
Six crore forty-two lakh fifteen thousand three hundred eight.
When reading a large number:
This method reduces mistakes.
Suppose the number is:
Seven crore twelve lakh five thousand forty-six.
Break it into groups:
Therefore:
7,00,00,000+12,00,000+5,000+467,00,00,000+12,00,000+5,000+46 =7,12,05,046=7,12,05,046
7,12,05,046\boxed{7,12,05,046}
Notice the zeroes in the thousands and hundreds places. They cannot simply be omitted.
Large numbers are not grouped in exactly the same way in all countries.
The Indian system commonly uses:
The International system commonly uses:
Consider:
10,00,00010,00,000
In the Indian system, this is:
Ten lakh.
In the International system, the same number is:
One million.
Thus:
10 lakh=1 million10\text{ lakh}=1\text{ million}
Similarly:
1 crore=10 million1\text{ crore}=10\text{ million}
because:
1,00,00,000=10,000,0001,00,00,000=10,000,000
| Indian System | International System |
|---|---|
| 1 thousand | 1 thousand |
| 1 lakh | 100 thousand |
| 10 lakh | 1 million |
| 1 crore | 10 million |
| 10 crore | 100 million |
| 100 crore | 1 billion |
These relationships are useful when interpreting information presented using different number systems.
To compare two large numbers, we should not start by comparing random digits.
A simple method is:
A number with more digits is larger.
For example:
8,75,0008,75,000
has six digits, while:
75,00075,000
has five digits.
Therefore:
8,75,000>75,0008,75,000>75,000
Consider:
6,45,0006,45,000
and
6,35,0006,35,000
Both contain six digits.
Compare the first digits:
6=66=6
Then compare the next digits:
4>34>3
Therefore:
6,45,000>6,35,0006,45,000>6,35,000
An exact value is the actual value.
An approximate value is a value that is close to the actual value and is easier to use.
For example, suppose a stadium has exactly:
48,76348,763
seats.
The exact number is:
48,76348,763
But for a quick estimate, we might say:
about 49,000\text{about }49,000
The second number is an approximation.
Approximation is helpful when:
Rounding means replacing a number with a nearby simpler number.
For example:
48,76348,763
rounded to the nearest thousand is:
49,00049,000
Why?
Look at the hundreds digit.
In 48,763, the hundreds digit is 7.
Since 7 is 5 or greater, we increase the thousands digit by 1.
Thus:
48,763≈49,00048,763\approx49,000
When rounding to a particular place:
Round:
6,43,7826,43,782
to the nearest thousand.
The thousands digit is 3.
The hundreds digit is 7.
Since:
7≥57\ge5
increase 3 to 4.
Therefore:
6,43,782≈6,44,0006,43,782\approx6,44,000
6,44,000\boxed{6,44,000}
Consider:
8,47,3218,47,321
We want the nearest lakh.
The lakh digit is 4.
The next digit, the ten-thousands digit, is 4.
Since 4 is less than 5, the lakh digit remains unchanged.
Therefore:
8,47,321≈8,00,0008,47,321\approx8,00,000
8,00,000\boxed{8,00,000}
Round:
8,67,3218,67,321
to the nearest lakh.
The lakh digit is 6.
The next digit is 6.
Since 6 is greater than 5, increase 6 to 7.
Therefore:
8,67,321≈9,00,0008,67,321\approx9,00,000
9,00,000\boxed{9,00,000}
Estimation means finding a value that is close enough to the actual answer to make calculation easier.
Suppose we need to estimate:
4,89,237+3,72,5144,89,237+3,72,514
We can round both numbers to the nearest lakh.
4,89,237≈5,00,0004,89,237\approx5,00,000
and
3,72,514≈4,00,0003,72,514\approx4,00,000
Therefore:
5,00,000+4,00,0005,00,000+4,00,000 =9,00,000=9,00,000
So the estimated sum is:
9,00,000\boxed{9,00,000}
The exact sum may be different, but the estimate gives us a quick idea of the size of the answer.
Suppose you calculate an answer and obtain:
90,00,00090,00,000
while a quick estimate suggests that the result should be around:
9,00,0009,00,000
There is probably a calculation error.
Therefore, estimation can also be used as a checking tool.
A number can be understood by identifying nearby numbers.
For example, consider:
5,00,0005,00,000
Numbers around it might include:
4,00,000,5,00,000,6,00,0004,00,000,\quad 5,00,000,\quad 6,00,000
If a number is:
5,42,0005,42,000
it is closer to:
5,00,0005,00,000
than to:
6,00,000.6,00,000.
Thinking about nearby values helps students understand estimation and rounding instead of treating rounding as a rule to memorise blindly.
Large-number calculations can sometimes become easier when we notice patterns.
For example:
25×4=10025\times4=100
Therefore:
250×4=1000250\times4=1000
and:
2500×4=100002500\times4=10000
The pattern is created by the extra zeroes.
Similarly:
125×8=1000125\times8=1000
so:
1,250×8=10,0001,250\times8=10,000
and:
12,500×8=1,00,00012,500\times8=1,00,000
Recognising such patterns can make calculations faster and help students understand multiplication rather than relying only on long written calculations.
Write:
5,24,07,3155,24,07,315
in words using the Indian system.
Separate the number:
Therefore:
Five crore twenty-four lakh seven thousand three hundred fifteen.
Five crore twenty-four lakh seven thousand three hundred fifteen\boxed{\text{Five crore twenty-four lakh seven thousand three hundred fifteen}}
Write three crore forty-five lakh six thousand twenty in figures.
Three crore:
3,00,00,0003,00,00,000
Forty-five lakh:
45,00,00045,00,000
Six thousand:
6,0006,000
Twenty:
2020
Combining them:
3,45,06,0203,45,06,020
3,45,06,020\boxed{3,45,06,020}
Which is greater?
7,45,23,1007,45,23,100
or
7,54,12,9007,54,12,900
Both numbers have the same number of digits.
Compare from the left:
Since:
5>45>4
we get:
7,54,12,900>7,45,23,1007,54,12,900>7,45,23,100
7,54,12,900\boxed{7,54,12,900}
is greater.
Round:
3,68,4523,68,452
to the nearest thousand.
The thousands digit is 8.
The hundreds digit is 4.
Since 4 is less than 5, the thousands digit remains 8.
Therefore:
3,68,452≈3,68,0003,68,452\approx3,68,000
3,68,000\boxed{3,68,000}
Round:
7,63,4507,63,450
to the nearest lakh.
The lakh digit is 7.
The ten-thousands digit is 6.
Since:
6>56>5
increase 7 to 8.
Therefore:
7,63,450≈8,00,0007,63,450\approx8,00,000
8,00,000\boxed{8,00,000}
Estimate:
6,24,700+2,81,4006,24,700+2,81,400
to the nearest lakh.
Round each number:
6,24,700≈6,00,0006,24,700\approx6,00,000 2,81,400≈3,00,0002,81,400\approx3,00,000
Now add:
6,00,000+3,00,000=9,00,0006,00,000+3,00,000=9,00,000
9,00,000\boxed{9,00,000}
Students sometimes write:
4,56,7894,56,789
as:
45,678945,6789
This is incorrect in the Indian system.
The correct form is:
4,56,7894,56,789
Remember:
10 lakh=1 million10\text{ lakh}=1\text{ million}
Therefore:
1 lakh=0.1 million1\text{ lakh}=0.1\text{ million}
Do not decide whether to round up merely by looking at the digit you are rounding.
Always check the digit immediately to its right.
If a question asks for an estimate, an approximate answer is expected.
If it asks for the exact value, do not round unnecessarily.
For example:
Four crore five lakh six thousand two hundred
must include the zeroes required by place value:
4,05,06,2004,05,06,200
The zeroes are important because they preserve the correct positions.
A student preparing this chapter should be able to:
A good revision session should include both direct questions and questions that require reasoning.
Uses units such as:
thousand → lakh → crore → arab
Uses:
thousand → million → billion → trillion
Finding a reasonably close value to make calculations easier.
Replacing a number by a nearby simpler number.
Using relationships between numbers to make calculations easier and discover mathematical rules.
A science exhibition receives 3,48,725 visitors during its first phase and 2,67,480 visitors during its second phase.
Find:
This question tests addition of large numbers and estimation.
3,48,725+2,67,4803,48,725+2,67,480
Add:
3,48,7253,48,725 +2,67,480+2,67,480 =6,16,205=6,16,205
Therefore, the exact total is:
6,16,205\boxed{6,16,205}
Round:
3,48,725≈3,00,0003,48,725\approx3,00,000
because the ten-thousands digit is 4.
Round:
2,67,480≈3,00,0002,67,480\approx3,00,000
because the ten-thousands digit is 6.
Therefore:
3,00,000+3,00,000=6,00,0003,00,000+3,00,000=6,00,000
Exact total:
6,16,205\boxed{6,16,205}
Estimated total:
6,00,000\boxed{6,00,000}
A district has a population of 8,72,450 people.
This question tests number reading and rounding.
8,72,4508,72,450
is:
Eight lakh seventy-two thousand four hundred fifty.
The lakh digit is 8.
The ten-thousands digit is 7.
Since:
7>57>5
increase 8 to 9.
Therefore:
8,72,450≈9,00,0008,72,450\approx9,00,000
The thousands digit is 2.
The hundreds digit is 4.
Since 4 is less than 5, the thousands digit remains unchanged.
Therefore:
8,72,450≈8,72,0008,72,450\approx8,72,000
Number name: Eight lakh seventy-two thousand four hundred fifty.
Nearest lakh:
9,00,000\boxed{9,00,000}
Nearest thousand:
8,72,000\boxed{8,72,000}
The current NCERT Grade 7 Mathematics Chapter 1 is Large Numbers Around Us in Ganita Prakash Part I.
The chapter introduces large quantities and develops understanding of lakhs, crores, millions and billions. It also deals with reading and writing large numbers, number systems, approximation, estimation and numerical patterns. NCERT describes the chapter as an introduction to lakhs and crores, and millions and billions through explorations and contexts.
1,00,000\boxed{1,00,000}
100 lakh\boxed{100\text{ lakh}}
because:
100×1,00,000=1,00,00,000100\times1,00,000=1,00,00,000
10 million\boxed{10\text{ million}}
An exact value represents the actual quantity, while an approximate value is a nearby value used when an exact number is unnecessary or when quick calculation is preferred.
Estimation helps students calculate quickly and check whether an exact answer is reasonable.
First understand place value and number systems. Then practise reading and writing large numbers, comparing them, rounding them and estimating calculations.
No. Use solutions to understand the method. After studying an example, close the solution and try a similar problem independently.
SyllabusStudy.in can build the following supporting resources around this chapter:
A strong way to study this chapter is:
Understand place value
↓
Learn Indian and International number systems
↓
Practise reading and writing numbers
↓
Compare numbers
↓
Learn rounding
↓
Practise estimation
↓
Study number patterns
↓
Attempt textbook questions independently
↓
Check the solution
↓
Take a practice test
This approach is more effective than memorising a list of answers.
Class 7 Maths Chapter 1 – Large Numbers Around Us builds an important foundation for working with large quantities. Students learn to understand numbers beyond the familiar thousands, work with lakhs and crores, relate them to millions and billions, and use estimation and rounding in practical situations.
The most useful habit in this chapter is to understand why a number is written, compared or rounded in a particular way. Once place value becomes clear, large-number calculations become much easier.
For exam preparation, combine concept revision with independent practice. Do not rely only on solution reading: attempt questions yourself, check your mistakes and then solve similar problems again.
The current textbook information in this article has been checked against the official NCERT Ganita Prakash, Textbook of Mathematics, Grade 7, Part I, Reprint 2026–27. NCERT identifies Chapter 1 as Large Numbers Around Us.
The article’s explanations and practice questions are independently written for SyllabusStudy.in and are not reproduced from the textbook.
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