Large Numbers — Lakhs and Crores

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Introduction — Why Do We Need Large Numbers?

In Class 4, you learned about numbers up to 9,99,999 (nine lakh ninety-nine thousand nine hundred and ninety-nine). But think about this: India's population is more than 140 crore! The distance from the Earth to the Moon is about 3,84,400 kilometres. ISRO's Chandrayaan-3 mission cost about 615 crore rupees. To talk about such large quantities, we need numbers that go beyond lakhs — we need crores!

In Class 5, we will learn to read, write, and work with numbers up to 9,99,99,999 (nine crore ninety-nine lakh ninety-nine thousand nine hundred and ninety-nine). We will also learn two different ways to name large numbers — the Indian Number System and the International Number System.

The Indian Number System — Place Value Chart

In the Indian Number System, we group digits starting from the right. The first group (Ones) has 3 digits, and every group after that has 2 digits. The place values are:

Crores (Cr) Ten Lakhs (TL) Lakhs (L) Ten Thousands (TTh) Thousands (Th) Hundreds (H) Tens (T) Ones (O)
10,00,00,000 10,00,000 1,00,000 10,000 1,000 100 10 1
Crores Period Lakhs Period Thousands Period Ones
Image needed: A colourful Indian Number System place value chart showing all 8 places from Ones to Crores. Each period (Ones, Thousands, Lakhs, Crores) highlighted in different colours. Arrows showing groups of digits. The number 5,32,48,671 placed in the chart as an example.
Style: Clean flat illustration, bright colours, child-friendly, labelled clearly
Size: 800×450px

Understanding the Periods

In the Indian system, digits are grouped into periods:

Example: Let us place the number 4,56,78,923 in the place value chart.
CrTLLTThThHTO
45678923

We read this as: Four crore fifty-six lakh seventy-eight thousand nine hundred and twenty-three.

Comma Placement — Indian System

Commas help us read large numbers easily. In the Indian system, we place commas like this:

Rules for Placing Commas (Indian System)

  • The first comma comes after 3 digits from the right (separates Hundreds from Thousands).
  • After that, place a comma after every 2 digits.
Examples:
Number (without commas)With commas (Indian)Number Name
234567823,45,678Twenty-three lakh forty-five thousand six hundred and seventy-eight
500000005,00,00,000Five crore
912345679,12,34,567Nine crore twelve lakh thirty-four thousand five hundred and sixty-seven
789012378,90,123Seventy-eight lakh ninety thousand one hundred and twenty-three
100500301,00,50,030One crore fifty thousand and thirty
Think About It: Why do we use commas differently in India compared to other countries? It is because our number names are different! We say "lakh" (1,00,000) while other countries say "hundred thousand" (100,000). The comma placement matches our way of reading numbers.

The International Number System

The International Number System is used in most countries around the world (USA, UK, Australia, etc.). In this system, digits are grouped in sets of 3 from the right. The place values are:

Ten Millions (TM) Millions (M) Hundred Thousands (HTh) Ten Thousands (TTh) Thousands (Th) Hundreds (H) Tens (T) Ones (O)
10,000,000 1,000,000 100,000 10,000 1,000 100 10 1
Millions Period Thousands Period Ones Period
Image needed: A colourful International Number System place value chart showing all 8 places from Ones to Ten Millions. Groups of 3 digits highlighted in different colours. The number 53,248,671 placed in the chart as an example.
Style: Clean flat illustration, bright colours, child-friendly, labelled clearly
Size: 800×450px

Understanding the Periods (International)

Example: The number 45,678,923 in the International system.
TMMHThTThThHTO
45678923

We read this as: Forty-five million six hundred seventy-eight thousand nine hundred and twenty-three.

Comma Placement — International System

Rules for Placing Commas (International System)

  • Place a comma after every 3 digits from the right.
  • This means commas come after Hundreds, and then after every group of three digits.
Examples:
Number (without commas)With commas (International)Number Name
23456782,345,678Two million three hundred forty-five thousand six hundred seventy-eight
5000000050,000,000Fifty million
9123456791,234,567Ninety-one million two hundred thirty-four thousand five hundred sixty-seven
78901237,890,123Seven million eight hundred ninety thousand one hundred twenty-three
1005003010,050,030Ten million fifty thousand and thirty

Comparison: Indian vs International Number System

Both systems use the same digits and the same value — only the way we name and group numbers is different. Here is a side-by-side comparison:

Number Indian System (with commas) Indian Name International System (with commas) International Name
100000 1,00,000 One Lakh 100,000 One Hundred Thousand
1000000 10,00,000 Ten Lakh 1,000,000 One Million
10000000 1,00,00,000 One Crore 10,000,000 Ten Million
50000000 5,00,00,000 Five Crore 50,000,000 Fifty Million
99999999 9,99,99,999 Nine Crore Ninety-Nine Lakh Ninety-Nine Thousand Nine Hundred Ninety-Nine 99,999,999 Ninety-Nine Million Nine Hundred Ninety-Nine Thousand Nine Hundred Ninety-Nine
Image needed: A visual comparison showing the same number (e.g., 3,25,47,000 vs 32,547,000) written in both Indian and International format side by side. Use two columns with colour-coded grouping to show how the same digits are grouped differently.
Style: Infographic style, split layout, colourful with arrows showing grouping
Size: 750×400px

Key Relationships to Remember

  • 1 Lakh = 100 Thousand (1,00,000 = 100,000)
  • 10 Lakhs = 1 Million (10,00,000 = 1,000,000)
  • 1 Crore = 10 Million (1,00,00,000 = 10,000,000)
  • 10 Crores = 100 Million (10,00,00,000 = 100,000,000)

Reading Large Numbers

When reading large numbers, commas act as helpful "pause points." We read the number period by period, from left to right.

Reading in the Indian System

Example 1: Read 3,45,67,890
Break it into periods: 3 (crore) | 45 (lakh) | 67 (thousand) | 890 (ones)
Read: Three crore forty-five lakh sixty-seven thousand eight hundred and ninety
Example 2: Read 7,08,00,501
Break it into periods: 7 (crore) | 08 (lakh) | 00 (thousand) | 501 (ones)
Read: Seven crore eight lakh five hundred and one
(Note: We skip "zero thousand" — we don't read zeros in the middle unless they have a value.)
Example 3: Read 6,00,40,020
Read: Six crore forty thousand and twenty

Reading in the International System

Example 4: Read 34,567,890
Break it into periods: 34 (million) | 567 (thousand) | 890 (ones)
Read: Thirty-four million five hundred sixty-seven thousand eight hundred ninety
Example 5: Read 70,800,501
Read: Seventy million eight hundred thousand five hundred one

Expanded Form of Large Numbers

The expanded form shows the value of each digit based on its place value. We multiply each digit by its place value and write them all added together.

Example 1: Write 4,56,78,923 in expanded form.

4,56,78,923 = 4 × 1,00,00,000 + 5 × 10,00,000 + 6 × 1,00,000 + 7 × 10,000 + 8 × 1,000 + 9 × 100 + 2 × 10 + 3 × 1

= 4,00,00,000 + 50,00,000 + 6,00,000 + 70,000 + 8,000 + 900 + 20 + 3
Example 2: Write 8,03,05,007 in expanded form.

8,03,05,007 = 8 × 1,00,00,000 + 0 × 10,00,000 + 3 × 1,00,000 + 0 × 10,000 + 5 × 1,000 + 0 × 100 + 0 × 10 + 7 × 1

= 8,00,00,000 + 3,00,000 + 5,000 + 7
(We skip the terms with 0 value.)
Example 3 (International): Write 45,678,923 in expanded form.

45,678,923 = 4 × 10,000,000 + 5 × 1,000,000 + 6 × 100,000 + 7 × 10,000 + 8 × 1,000 + 9 × 100 + 2 × 10 + 3 × 1

From Expanded Form to Standard Form

Example 4: Write in standard form: 3 × 1,00,00,000 + 7 × 10,00,000 + 0 × 1,00,000 + 4 × 10,000 + 2 × 1,000 + 6 × 100 + 0 × 10 + 5 × 1

= 3,00,00,000 + 70,00,000 + 0 + 40,000 + 2,000 + 600 + 0 + 5
= 3,70,42,605

Comparing Large Numbers

When comparing large numbers, follow these rules in order:

Rules for Comparing Numbers

  • Rule 1: The number with more digits is always greater.
    Example: 1,00,00,000 (8 digits) > 99,99,999 (7 digits)
  • Rule 2: If both numbers have the same number of digits, compare digit by digit from the left.
    Start from the leftmost digit. The number with a larger digit at the first differing position is greater.
Example 1: Compare 5,43,21,678 and 5,43,25,678
Both have 8 digits. Compare from left:
5 = 5 ✓ | 4 = 4 ✓ | 3 = 3 ✓ | 2 = 2 ✓ | 1 < 5
So, 5,43,21,678 < 5,43,25,678
Example 2: Compare 7,89,45,123 and 7,89,45,123
All digits are exactly the same.
So, 7,89,45,123 = 7,89,45,123
Example 3: Arrange in ascending order: 3,45,67,890 ; 3,45,68,000 ; 3,44,99,999
All are 8-digit numbers. Compare from left:
- All start with 3,4...
- Third digit: 5, 5, 4 → 3,44,99,999 is smallest
- Between the other two: 3,45,67,890 vs 3,45,68,000 → 7 < 8
Ascending order: 3,44,99,999 < 3,45,67,890 < 3,45,68,000

Forming the Greatest and Smallest Numbers

Example 4: Using digits 7, 0, 3, 5, 2, 9, 1, 8 (each used once), form:
Greatest 8-digit number: Arrange digits in descending order → 9,87,53,210
Smallest 8-digit number: Arrange digits in ascending order (but 0 cannot be first!) → 1,02,35,789

Predecessor and Successor

The predecessor of a number is 1 less than that number (the number that comes just before it). The successor of a number is 1 more than that number (the number that comes just after it).

Remember

  • Predecessor = Number − 1
  • Successor = Number + 1
Examples:
NumberPredecessor (−1)Successor (+1)
5,00,00,0004,99,99,9995,00,00,001
1,00,00,00099,99,9991,00,00,001
9,99,99,9999,99,99,99810,00,00,000
3,50,00,0003,49,99,9993,50,00,001
7,00,00,0017,00,00,0007,00,00,002
Think About It: Notice how finding the predecessor of 1,00,00,000 gives us a 7-digit number (99,99,999). Similarly, the successor of 9,99,99,999 gives us a 9-digit number (10,00,00,000)! This is called "crossing a digit boundary."

Real-Life Examples of Large Numbers

Large numbers are everywhere around us! Let us look at some real-life examples from India:

FactNumber (Indian System)Number (International System)
Population of India (approx.)1,40,00,00,000 (140 crore)1,400,000,000 (1.4 billion)
Population of Mumbai2,10,00,000 (2 crore 10 lakh)21,000,000 (21 million)
Cost of Chandrayaan-3 (ISRO)₹6,15,00,00,000 (615 crore)₹6,150,000,000
Distance: Earth to Moon3,84,400 km384,400 km
Distance: Earth to Sun15,00,00,000 km (15 crore)150,000,000 km (150 million)
Indian Railways passengers per day2,30,00,000 (2 crore 30 lakh)23,000,000 (23 million)
Highest score in IPL history287 runs (RCB vs PWI, 2013)287 runs
Image needed: An infographic showing real-life large numbers in India — India's population (stick figures), ISRO rocket with budget label, train with passenger count, Moon with distance. All numbers shown in Indian system with commas.
Style: Colourful infographic, child-friendly icons, clean layout
Size: 800×500px
Let's Practice Reading:
Arjun read in the newspaper that Indian Railways earned ₹2,40,000 crore in the last year. His teacher asked him to write this number.

₹2,40,000 crore = ₹2,40,000 × 1,00,00,000 = ₹24,00,00,00,00,000
(This is beyond crores — it is in the "lakh crore" range! We will learn these in higher classes.)

Key Words

TermMeaning
Place ValueThe value of a digit based on its position in the number
Face ValueThe digit itself, regardless of its position
PeriodA group of digits separated by commas (Ones, Thousands, Lakhs, Crores)
Lakh1,00,000 (one hundred thousand)
Crore1,00,00,000 (ten million)
Million1,000,000 (ten lakh)
Expanded FormA number written as the sum of the values of each digit
Standard FormThe normal way of writing a number (e.g., 4,56,78,923)
PredecessorThe number that comes just before (number − 1)
SuccessorThe number that comes just after (number + 1)
Ascending OrderArranging numbers from smallest to largest
Descending OrderArranging numbers from largest to smallest

Key Points to Remember

  • In the Indian system: first comma after 3 digits from right, then after every 2 digits.
  • In the International system: comma after every 3 digits from the right.
  • 1 Lakh = 100 Thousand | 10 Lakhs = 1 Million | 1 Crore = 10 Million
  • The largest 7-digit number is 99,99,999 (Ninety-nine lakh ninety-nine thousand nine hundred ninety-nine).
  • The smallest 8-digit number is 1,00,00,000 (One crore).
  • The largest 8-digit number is 9,99,99,999 (Nine crore ninety-nine lakh ninety-nine thousand nine hundred ninety-nine).
  • When comparing numbers: more digits = greater number. Same digits = compare from left.
  • Place value of a digit = Face value × Value of its position.
  • The value of the number does NOT change between Indian and International systems — only the way we read and write it changes.

Finished learning? Now test what you know!