Class 7MathematicsChapter 1NCERT • Ganita Prakash

Large Numbers Around Us

Learn how to read, compare, estimate and work confidently with lakhs, crores, millions and billions.

Chapter Snapshot

Place value helps us understand large numbers.
The Indian system uses lakh and crore.
The International system uses million and billion.
Large numbers can be written in expanded form.
Rounding gives a nearby simpler number.
Estimation helps us check answers quickly.
Number patterns can make calculations easier.

What You Will Learn

Read and write large numbers
Understand face value and place value
Write numbers in expanded form
Use Indian and International number systems
Compare large numbers
Round numbers to suitable place values
Estimate sums and differences

Exam PriorityBoardsVery HighFoundationHigh

Chapter Overview

Large numbers are used in everyday life to describe populations, money, distances, data and many other quantities.

For example:

a school may have 2,000 students;
a city may have several lakh people;
a country may have a population of many crores.

Understanding place value makes such numbers easier to read and compare.

1. Place Value

Each position in a number has a value.

Moving one place to the left makes the value 10 times greater.

Place Value Pattern

1 \times 10 = 10

Therefore:

1{,}00{,}000 = 1 \text{ lakh}

and:

1{,}00{,}00{,}000 = 1 \text{ crore}

2. Face Value and Place Value

Face Value vs Place Value

Feature	Face Value	Place Value
Meaning	Digit itself	Value based on position
6 in 6,42,315	6	6,00,000

Quick Check

What is the place value of 5 in 3,56,210?

Show answer

50,000

3. Expanded Form

Expanded form shows a number as the sum of its place values.

For example:

6{,}42{,}805 = 6{,}00{,}000 + 40{,}000 + 2{,}000 + 800 + 5

Expanded Form

Question

Write 7,46,205 in expanded form.

Solution

7{,}46{,}205 = 7{,}00{,}000 + 40{,}000 + 6{,}000 + 200 + 5

4. Indian Number System

The important large-number places are:

thousand;
ten thousand;
lakh;
ten lakh;
crore;
ten crore.

Indian Place Values

Place	Value
Thousand	1,000
Ten Thousand	10,000
Lakh	1,00,000
Ten Lakh	10,00,000
Crore	1,00,00,000
Ten Crore	10,00,00,000

Indian Comma Rule

In the Indian system:

first group 3 digits from the right;
after that, group digits in pairs.

Example:

76543219

becomes:

7,65,43,219

Read as:

Seven crore sixty-five lakh forty-three thousand two hundred nineteen.

5. International Number System

The International system uses:

thousand;
million;
billion.

Digits are grouped in sets of three from the right.

Example:

9876501234

becomes:

9,876,501,234

Indian vs International System

Value	Indian System	International System
1,00,000	1 lakh	100 thousand
10,00,000	10 lakh	1 million
1,00,00,000	1 crore	10 million
1,00,00,00,000	1 arab	1 billion

6. Important Conversions

Formula / Key Relations

1 \text{ million} = 10 \text{ lakh}

Million to Lakh

Question

Convert 8 million into lakhs.

Solution

1 \text{ million} = 10 \text{ lakh}

7. Comparing Large Numbers

Follow these simple rules:

The number with more digits is greater.
If both have the same number of digits, compare from the left.

Compare Large Numbers

Question

Which is greater: 7,86,435 or 7,68,945?

Solution

7{,}86{,}435 > 7{,}68{,}945

Quick Check

Which is greater: 5,93,281 or 5,92,999?

Show answer

5,93,281

8. Rounding Large Numbers

Rounding gives a nearby, simpler number.

Rule

Next digit 5 or more → round up.
Next digit less than 5 → keep the digit unchanged.

Nearest Thousand

Round 48,672 to the nearest thousand.

The hundreds digit is 6.

Since 6 is greater than 5:

48{,}672 \approx 49{,}000

Nearest Lakh

Round 6,72,340 to the nearest lakh.

The ten-thousands digit is 7.

Therefore:

6{,}72{,}340 \approx 7{,}00{,}000

9. Estimation

Estimation gives an approximate answer quickly.

Suppose:

4{,}63{,}128 + 4{,}19{,}682

Round to the nearest lakh:

4{,}63{,}128 \approx 5{,}00{,}000

4{,}19{,}682 \approx 4{,}00{,}000

So:

5{,}00{,}000 + 4{,}00{,}000 = 9{,}00{,}000

The actual answer should be close to 9 lakh.

10. Smart Multiplication

Some numbers can be multiplied quickly using simple relationships.

Multiplying by 5

Since:

5 = \frac{10}{2}

For:

84 \times 5

divide 84 by 2:

84 \div 2 = 42

then multiply by 10:

42 \times 10 = 420

Multiplying by 25

Since:

25 = \frac{100}{4}

For:

248 \times 25

first divide by 4:

248 \div 4 = 62

then:

62 \times 100 = 6{,}200

Multiplying by 125

Since:

125 = \frac{1000}{8}

Quick Multiplication

Question

Find 64 × 125.

Solution

64 \div 8 = 8

11. Number of Digits in a Product

The smallest 2-digit number is 10.

10 \times 10 = 100

So the product of two 2-digit numbers has at least 3 digits.

Also:

100 \times 100 = 10{,}000

Since 2-digit numbers are less than 100, their product is less than 10,000.

Therefore:

Important Terms

Key Terms

Face ValuePlace ValueExpanded FormLakhCroreMillionBillionIndian Number SystemInternational Number SystemRoundingEstimation

Common Mistakes

Exam Focus

Important Exam Topics

Prepare these carefully:

face value and place value;
expanded form;
Indian comma placement;
International comma placement;
lakh, crore, million and billion conversions;
comparison of large numbers;
rounding;
estimation;
multiplication by 5, 25 and 125.

Quick Revision

1 lakh = 1,00,000
1 crore = 1,00,00,000
100 lakh = 1 crore
1 million = 10 lakh
1 crore = 10 million
1 billion = 100 crore
Indian comma pattern: 3-2-2-2
International comma pattern: 3-3-3
Face value is the digit itself.
Place value depends on position.
Expanded form shows the value of each digit.
Compare numbers from the left.
Rounding gives a nearby simpler number.
Estimation helps check answers.
Multiplication can sometimes be simplified by regrouping.

Practice Questions

Multiple Choice Questions

Q1MCQEasyClass 7

One lakh is: A. 10,000 B. 1,00,000 C. 10,00,000 D. 1,00,00,000

View Solution

Answer: B. 1,00,000

Q2MCQEasyClass 7

One million equals: A. 1 lakh B. 10 lakh C. 100 lakh D. 1 crore

View Solution

1 \text{ million} = 10 \text{ lakh}

Q3MCQEasyClass 7

What is the place value of 6 in 4,63,218 ? A. 6 B. 600 C. 6,000 D. 60,000

View Solution

Answer: D. 60,000

Q4MCQModerateClass 7

Which is the correct Indian notation? A. 54,321,678 B. 5,43,21,678 C. 543,21,678 D. 5432,1678

View Solution

Answer: B. 5,43,21,678

Short Answer Questions

Q5Short AnswerEasyClass 7

Write 6,42,805 in expanded form.

View Solution

6{,}42{,}805 = 6{,}00{,}000 + 40{,}000 + 2{,}000 + 800 + 5

Q6Short AnswerEasyClass 7

Write 8,07,45,306 in words.

View Solution

Eight crore seven lakh forty-five thousand three hundred six.

Q7Short AnswerModerateClass 7

Convert 25 million into lakhs.

View Solution

1 \text{ million} = 10 \text{ lakh}

Numerical Questions

Q8NumericalModerateClass 7

Round 8,67,349 to the nearest lakh.

View Solution

8{,}67{,}349 \approx 9{,}00{,}000

Q9NumericalModerateClass 7

7{,}48{,}320 + 5{,}63{,}780

View Solution

7{,}48{,}320 \approx 7{,}00{,}000

Q10NumericalModerateFoundation

72 \times 125

View Solution

125 = \frac{1000}{8}

Apply Your Learning

Find any three large numbers around you.

They may come from:

population;
money;
sports;
distances;
school records.

For each number:

write it using Indian commas;
write it in words;
identify the place value of one digit;
round it to the nearest lakh.

Chapter Summary

Large numbers become easier when we understand place value.
Face value is the digit itself.
Place value depends on position.
Indian numbers use lakh and crore.
International numbers use million and billion.
1 million = 10 lakh.
1 crore = 10 million.
Large numbers are compared from left to right.
Rounding gives nearby simpler values.
Estimation helps check calculations.
Regrouping can make multiplication faster.

Class 7MathematicsChapter 1NCERT • Ganita Prakash

Large Numbers Around Us

Learn how to read, compare, estimate and work confidently with lakhs, crores, millions and billions.

Chapter Snapshot

Place value helps us understand large numbers.
The Indian system uses lakh and crore.
The International system uses million and billion.
Large numbers can be written in expanded form.
Rounding gives a nearby simpler number.
Estimation helps us check answers quickly.
Number patterns can make calculations easier.

What You Will Learn

Read and write large numbers
Understand face value and place value
Write numbers in expanded form
Use Indian and International number systems
Compare large numbers
Round numbers to suitable place values
Estimate sums and differences

Exam PriorityBoardsVery HighFoundationHigh

Chapter Overview

Large numbers are used in everyday life to describe populations, money, distances, data and many other quantities.

For example:

a school may have 2,000 students;
a city may have several lakh people;
a country may have a population of many crores.

Understanding place value makes such numbers easier to read and compare.

1. Place Value

Each position in a number has a value.

Moving one place to the left makes the value 10 times greater.

Place Value Pattern

1 \times 10 = 10

Therefore:

1{,}00{,}000 = 1 \text{ lakh}

and:

1{,}00{,}00{,}000 = 1 \text{ crore}

2. Face Value and Place Value

Face Value vs Place Value

Feature	Face Value	Place Value
Meaning	Digit itself	Value based on position
6 in 6,42,315	6	6,00,000

Quick Check

What is the place value of 5 in 3,56,210?

Show answer

50,000

3. Expanded Form

Expanded form shows a number as the sum of its place values.

For example:

6{,}42{,}805 = 6{,}00{,}000 + 40{,}000 + 2{,}000 + 800 + 5

Expanded Form

Question

Write 7,46,205 in expanded form.

Solution

7{,}46{,}205 = 7{,}00{,}000 + 40{,}000 + 6{,}000 + 200 + 5

4. Indian Number System

The important large-number places are:

thousand;
ten thousand;
lakh;
ten lakh;
crore;
ten crore.

Indian Place Values

Place	Value
Thousand	1,000
Ten Thousand	10,000
Lakh	1,00,000
Ten Lakh	10,00,000
Crore	1,00,00,000
Ten Crore	10,00,00,000

Indian Comma Rule

In the Indian system:

first group 3 digits from the right;
after that, group digits in pairs.

Example:

76543219

becomes:

7,65,43,219

Read as:

Seven crore sixty-five lakh forty-three thousand two hundred nineteen.

5. International Number System

The International system uses:

thousand;
million;
billion.

Digits are grouped in sets of three from the right.

Example:

9876501234

becomes:

9,876,501,234

Indian vs International System

Value	Indian System	International System
1,00,000	1 lakh	100 thousand
10,00,000	10 lakh	1 million
1,00,00,000	1 crore	10 million
1,00,00,00,000	1 arab	1 billion

6. Important Conversions

Formula / Key Relations

1 \text{ million} = 10 \text{ lakh}

Million to Lakh

Question

Convert 8 million into lakhs.

Solution

1 \text{ million} = 10 \text{ lakh}

7. Comparing Large Numbers

Follow these simple rules:

The number with more digits is greater.
If both have the same number of digits, compare from the left.

Compare Large Numbers

Question

Which is greater: 7,86,435 or 7,68,945?

Solution

7{,}86{,}435 > 7{,}68{,}945

Quick Check

Which is greater: 5,93,281 or 5,92,999?

Show answer

5,93,281

8. Rounding Large Numbers

Rounding gives a nearby, simpler number.

Rule

Next digit 5 or more → round up.
Next digit less than 5 → keep the digit unchanged.

Nearest Thousand

Round 48,672 to the nearest thousand.

The hundreds digit is 6.

Since 6 is greater than 5:

48{,}672 \approx 49{,}000

Nearest Lakh

Round 6,72,340 to the nearest lakh.

The ten-thousands digit is 7.

Therefore:

6{,}72{,}340 \approx 7{,}00{,}000

9. Estimation

Estimation gives an approximate answer quickly.

Suppose:

4{,}63{,}128 + 4{,}19{,}682

Round to the nearest lakh:

4{,}63{,}128 \approx 5{,}00{,}000

4{,}19{,}682 \approx 4{,}00{,}000

So:

5{,}00{,}000 + 4{,}00{,}000 = 9{,}00{,}000

The actual answer should be close to 9 lakh.

10. Smart Multiplication

Some numbers can be multiplied quickly using simple relationships.

Multiplying by 5

Since:

5 = \frac{10}{2}

For:

84 \times 5

divide 84 by 2:

84 \div 2 = 42

then multiply by 10:

42 \times 10 = 420

Multiplying by 25

Since:

25 = \frac{100}{4}

For:

248 \times 25

first divide by 4:

248 \div 4 = 62

then:

62 \times 100 = 6{,}200

Multiplying by 125

Since:

125 = \frac{1000}{8}

Quick Multiplication

Question

Find 64 × 125.

Solution

64 \div 8 = 8

11. Number of Digits in a Product

The smallest 2-digit number is 10.

10 \times 10 = 100

So the product of two 2-digit numbers has at least 3 digits.

Also:

100 \times 100 = 10{,}000

Since 2-digit numbers are less than 100, their product is less than 10,000.

Therefore:

Important Terms

Key Terms

Face ValuePlace ValueExpanded FormLakhCroreMillionBillionIndian Number SystemInternational Number SystemRoundingEstimation

Common Mistakes

Exam Focus

Important Exam Topics

Prepare these carefully:

face value and place value;
expanded form;
Indian comma placement;
International comma placement;
lakh, crore, million and billion conversions;
comparison of large numbers;
rounding;
estimation;
multiplication by 5, 25 and 125.

Quick Revision

1 lakh = 1,00,000
1 crore = 1,00,00,000
100 lakh = 1 crore
1 million = 10 lakh
1 crore = 10 million
1 billion = 100 crore
Indian comma pattern: 3-2-2-2
International comma pattern: 3-3-3
Face value is the digit itself.
Place value depends on position.
Expanded form shows the value of each digit.
Compare numbers from the left.
Rounding gives a nearby simpler number.
Estimation helps check answers.
Multiplication can sometimes be simplified by regrouping.

Practice Questions

Multiple Choice Questions

Q1MCQEasyClass 7

One lakh is: A. 10,000 B. 1,00,000 C. 10,00,000 D. 1,00,00,000

View Solution

Answer: B. 1,00,000

Q2MCQEasyClass 7

One million equals: A. 1 lakh B. 10 lakh C. 100 lakh D. 1 crore

View Solution

1 \text{ million} = 10 \text{ lakh}

Q3MCQEasyClass 7

What is the place value of 6 in 4,63,218 ? A. 6 B. 600 C. 6,000 D. 60,000

View Solution

Answer: D. 60,000

Q4MCQModerateClass 7

Which is the correct Indian notation? A. 54,321,678 B. 5,43,21,678 C. 543,21,678 D. 5432,1678

View Solution

Answer: B. 5,43,21,678

Short Answer Questions

Q5Short AnswerEasyClass 7

Write 6,42,805 in expanded form.

View Solution

6{,}42{,}805 = 6{,}00{,}000 + 40{,}000 + 2{,}000 + 800 + 5

Q6Short AnswerEasyClass 7

Write 8,07,45,306 in words.

View Solution

Eight crore seven lakh forty-five thousand three hundred six.

Q7Short AnswerModerateClass 7

Convert 25 million into lakhs.

View Solution

1 \text{ million} = 10 \text{ lakh}

Numerical Questions

Q8NumericalModerateClass 7

Round 8,67,349 to the nearest lakh.

View Solution

8{,}67{,}349 \approx 9{,}00{,}000

Q9NumericalModerateClass 7

7{,}48{,}320 + 5{,}63{,}780

View Solution

7{,}48{,}320 \approx 7{,}00{,}000

Q10NumericalModerateFoundation

72 \times 125

View Solution

125 = \frac{1000}{8}

Apply Your Learning

Find any three large numbers around you.

They may come from:

population;
money;
sports;
distances;
school records.

For each number:

write it using Indian commas;
write it in words;
identify the place value of one digit;
round it to the nearest lakh.

Chapter Summary

Large numbers become easier when we understand place value.
Face value is the digit itself.
Place value depends on position.
Indian numbers use lakh and crore.
International numbers use million and billion.
1 million = 10 lakh.
1 crore = 10 million.
Large numbers are compared from left to right.
Rounding gives nearby simpler values.
Estimation helps check calculations.
Regrouping can make multiplication faster.