Numbers up to Lakhs
Numbers up to lakhs form the foundation of the Indian number system taught in Class 5. In earlier classes, you worked with numbers up to 10,000 or 99,999. Now, you will learn about 6-digit numbers that go up to 9,99,999 (nine lakh, ninety-nine thousand, nine hundred and ninety-nine).
Understanding large numbers is essential for reading populations, distances, prices of land and vehicles, and many other real-life quantities. The Indian number system uses periods called Ones, Thousands, and Lakhs to group digits and make large numbers easy to read and write.
A lakh is a uniquely Indian term. While most countries say "one hundred thousand," in India we say "one lakh." This lesson will teach you how to read, write, expand, and work with numbers that go all the way up to lakhs.
By the end of this topic, you will be able to identify the number of digits in a large number, place any number in a place value chart, convert between standard form and expanded form, and find predecessors and successors of numbers up to lakhs.
What is Numbers up to Lakhs - Class 5 Maths (Large Numbers)?
A lakh (written as 1,00,000) is equal to one hundred thousand (100,000). Numbers up to lakhs include all numbers from 1,00,000 to 9,99,999. These are all 6-digit numbers.
In the Indian system, these 6-digit numbers are grouped as:
| Lakhs Period | Thousands Period | Ones Period | ||||
|---|---|---|---|---|---|---|
| T. Lakhs | Lakhs | T. Th. | Thousands | Hundreds | Tens | Ones |
| -- | 1 | 0 | 0 | 0 | 0 | 0 |
The number shown above is 1,00,000 -- read as "one lakh".
How commas work in the Indian system: Starting from the right, place the first comma after 3 digits (separating the ones period). After that, place a comma after every 2 digits. So for a 6-digit number like 456789, the Indian notation is 4,56,789.
Key terms:
- Face value: The digit itself. The face value of 7 is always 7.
- Place value: The value a digit holds because of its position. In 7,00,000, the place value of 7 is 7,00,000.
- Expanded form: A number written as the sum of the place values of each digit.
- Standard form: The usual way of writing a number (e.g., 4,56,032).
- Predecessor: The number that comes just before (subtract 1).
- Successor: The number that comes just after (add 1).
Numbers up to Lakhs Formula
1 Lakh = 1,00,000 = 100 Thousands = 10 Ten-Thousands
10 Lakhs = 10,00,000 = 1 Million
Complete place value chain:
- 1 Ten = 10 Ones
- 1 Hundred = 10 Tens = 100 Ones
- 1 Thousand = 10 Hundreds = 1,000 Ones
- 1 Ten Thousand = 10 Thousands = 10,000 Ones
- 1 Lakh = 10 Ten Thousands = 100 Thousands = 1,00,000 Ones
- 1 Ten Lakh = 10 Lakhs = 10,00,000 Ones
Types and Properties
5-digit numbers range from 10,000 to 99,999. They use places up to the ten-thousands place.
6-digit numbers range from 1,00,000 to 9,99,999. They introduce the lakhs place. This is the focus of this lesson.
7-digit numbers (briefly introduced) range from 10,00,000 to 99,99,999. They use the ten-lakhs place.
| Digits | Smallest | Largest | Total Count | Name of Range |
|---|---|---|---|---|
| 5-digit | 10,000 | 99,999 | 90,000 | Ten thousands |
| 6-digit | 1,00,000 | 9,99,999 | 9,00,000 | Lakhs |
| 7-digit | 10,00,000 | 99,99,999 | 90,00,000 | Ten lakhs |
Important relationships:
- The successor of the largest 5-digit number (99,999) is the smallest 6-digit number (1,00,000).
- The successor of the largest 6-digit number (9,99,999) is the smallest 7-digit number (10,00,000).
- Each new digit count starts where the previous one ended, plus one.
How to form the largest and smallest numbers from given digits:
- Largest number: Arrange all digits in descending order (biggest first).
- Smallest number: Arrange all digits in ascending order. If 0 is among the digits, it cannot be the first digit -- swap it with the smallest non-zero digit.
Solved Examples
Example 1: Example 1: Identify the Number of Digits
Problem: How many digits does the number 3,45,678 have? Identify the period of each digit.
Solution:
Step 1: Count the digits: 3, 4, 5, 6, 7, 8 -- there are 6 digits.
Step 2: Place each digit in the place value chart:
| Lakhs | T. Th. | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
| 3 | 4 | 5 | 6 | 7 | 8 |
Step 3: Identify the periods:
- Digit 3 is in the Lakhs period
- Digits 4 and 5 are in the Thousands period
- Digits 6, 7, and 8 are in the Ones period
Answer: 3,45,678 is a 6-digit number. The digit 3 is in the lakhs period, digits 4 and 5 are in the thousands period, and digits 6, 7, 8 are in the ones period.
Example 2: Example 2: Write the Number Name
Problem: Write the number name of 5,07,230.
Solution:
Step 1: Split into periods using commas: 5 | 07 | 230
Step 2: Read each period from left to right:
- Lakhs period: 5 → Five lakh
- Thousands period: 07 → Seven thousand (we skip the 0 in the ten-thousands place)
- Ones period: 230 → Two hundred and thirty
Step 3: Combine all parts.
Answer: Five lakh seven thousand two hundred and thirty.
Example 3: Example 3: Write in Figures from Number Name
Problem: Write in figures: Eight lakh forty-two thousand six hundred and fifteen.
Solution:
Step 1: Convert each period to digits:
- Eight lakh = 8,00,000
- Forty-two thousand = 42,000
- Six hundred and fifteen = 615
Step 2: Add all values: 8,00,000 + 42,000 + 615 = 8,42,615
Step 3: Verify by checking digit count: 8,42,615 has 6 digits -- correct for a number in lakhs.
Answer: 8,42,615
Example 4: Example 4: Find the Place Value of a Digit
Problem: What is the place value of 7 in the number 7,63,489?
Solution:
Step 1: Locate the digit 7. It is the leftmost digit, which means it is in the lakhs place.
Step 2: Place value = Face value x Position value = 7 x 1,00,000 = 7,00,000
Step 3: In words, this is "seven lakh."
Answer: The place value of 7 is 7,00,000 (seven lakh).
Example 5: Example 5: Expanded Form
Problem: Write 4,56,032 in expanded form.
Solution:
Step 1: Identify each digit and its position:
| Digit | Place | Place Value |
|---|---|---|
| 4 | Lakhs | 4,00,000 |
| 5 | Ten Thousands | 50,000 |
| 6 | Thousands | 6,000 |
| 0 | Hundreds | 0 |
| 3 | Tens | 30 |
| 2 | Ones | 2 |
Step 2: Write as a sum of place values (skip the 0):
4,56,032 = 4,00,000 + 50,000 + 6,000 + 30 + 2
Answer: 4,00,000 + 50,000 + 6,000 + 30 + 2
Example 6: Example 6: Standard Form from Expanded Form
Problem: Write the standard form: 2,00,000 + 30,000 + 8,000 + 400 + 50 + 1
Solution:
Step 1: Add all the values step by step:
- 2,00,000 + 30,000 = 2,30,000
- 2,30,000 + 8,000 = 2,38,000
- 2,38,000 + 400 = 2,38,400
- 2,38,400 + 50 = 2,38,450
- 2,38,450 + 1 = 2,38,451
Step 2: Alternatively, just assign each value to its correct place in the place value chart. All six places are accounted for, so no zeros are needed.
Answer: 2,38,451
Example 7: Example 7: Forming the Largest and Smallest Numbers
Problem: Using the digits 5, 0, 3, 8, 1, 7 (each used once), form the largest and smallest 6-digit numbers.
Solution:
Largest number:
Step 1: Arrange digits in descending order: 8, 7, 5, 3, 1, 0
Step 2: The number is 8,75,310.
Smallest number:
Step 1: Arrange digits in ascending order: 0, 1, 3, 5, 7, 8
Step 2: The first digit cannot be 0 (a 6-digit number cannot start with 0). Swap 0 with the next smallest digit (1).
Step 3: The number is 1,03,578.
Answer: Largest = 8,75,310, Smallest = 1,03,578
Example 8: Example 8: Predecessor and Successor
Problem: Find the predecessor and successor of 3,00,000.
Solution:
Predecessor: The number that comes just before 3,00,000.
Predecessor = 3,00,000 - 1 = 2,99,999
Notice: The predecessor is a 6-digit number, but the lakhs digit changes from 3 to 2, and all other digits become 9.
Successor: The number that comes just after 3,00,000.
Successor = 3,00,000 + 1 = 3,00,001
Answer: Predecessor = 2,99,999, Successor = 3,00,001
Example 9: Example 9: Real-Life Word Problem
Problem: The population of Aman's town is 2,34,500. The neighbouring town has a population of 1,87,300. What is the total population of both towns?
Solution:
Step 1: Write the addition in column form, aligning place values:
2,34,500
+ 1,87,300
---------
4,21,800
Step 2: Add column by column from right to left:
- Ones: 0+0=0. Tens: 0+0=0. Hundreds: 5+3=8.
- Thousands: 4+7=11. Write 1, carry 1.
- T.Th: 3+8+1=12. Write 2, carry 1.
- Lakhs: 2+1+1=4.
Answer: The total population is 4,21,800 (Four lakh twenty-one thousand eight hundred).
Example 10: Example 10: Face Value vs Place Value
Problem: Find the difference between the place value and the face value of 6 in 6,54,321.
Solution:
Step 1: Face value of 6 = 6 (the digit itself, regardless of position).
Step 2: The digit 6 is in the lakhs place.
Place value of 6 = 6 x 1,00,000 = 6,00,000 (six lakh).
Step 3: Difference = Place value - Face value = 6,00,000 - 6 = 5,99,994
Answer: The difference is 5,99,994.
Real-World Applications
Numbers up to lakhs appear everywhere in daily life:
- Population: A city's population can be expressed as 5,00,000 or more. When we say "the population of Jaipur is about 30 lakh," we are using numbers in lakhs.
- Prices: A car may cost ₹6,50,000. A plot of land may cost ₹9,00,000. Understanding lakhs is essential for reading price tags on expensive items.
- Distances: The distance between two cities can exceed 1,00,000 metres. When engineers measure large distances, they work with numbers in lakhs.
- Bank accounts: Savings accounts, fixed deposits, and loan amounts are often in lakhs. Your parents might say, "We have ₹3,50,000 in savings."
- School data: A school chain like Orchids International School has over 1,00,000 students across all branches. Managing such data requires comfort with large numbers.
- Sports: A cricket stadium can seat 1,32,000 people. Total runs scored by a team in a series can cross 1,00,000.
Key Points to Remember
- The Indian number system groups digits into periods: Ones (3 digits), Thousands (2 digits), and Lakhs (2 digits).
- A 6-digit number ranges from 1,00,000 to 9,99,999.
- 1 lakh = 1,00,000 = 100 thousands = 10 ten-thousands.
- 10 lakhs = 10,00,000 = 1 million.
- The place value of a digit depends on its position; the face value is the digit itself.
- In the Indian system, commas are placed after the first 3 digits from the right, then after every 2 digits: e.g., 5,67,890.
- The predecessor of a number is 1 less than it; the successor is 1 more.
- To form the smallest number from given digits, arrange in ascending order. If 0 is present, it cannot be the first digit -- place the smallest non-zero digit first.
- To form the largest number, arrange digits in descending order.
- The expanded form of a number shows it as the sum of the place values of all its digits.
Practice Problems
- Write the number name of 7,08,456.
- Write in figures: Three lakh sixty thousand nine hundred and twelve.
- Find the place value of 4 in the number 4,92,175.
- Write the expanded form of 6,05,840.
- Using digits 9, 2, 0, 4, 7, 6, form the largest and smallest 6-digit numbers (each digit used once).
- Find the predecessor and successor of 5,99,999. What can you say about the number of digits in each?
- Priya's school collected ₹3,25,000 for charity. Another school collected ₹2,78,500. What is the total amount collected?
- What is the difference between the place value and face value of 3 in 3,41,209?
Frequently Asked Questions
Q1. What does 1 lakh mean?
1 lakh equals 1,00,000 (one hundred thousand). It is the first 6-digit number in the Indian number system. The word "lakh" comes from the Sanskrit word "laksha." In daily life, we use lakhs for large amounts like car prices, salaries, and populations.
Q2. How many zeros are there in 1 lakh?
There are 5 zeros in 1 lakh. Written out: 1,00,000. Each zero represents an empty place -- ones, tens, hundreds, thousands, and ten-thousands are all zero.
Q3. What is the smallest 6-digit number?
The smallest 6-digit number is 1,00,000 (one lakh). It comes right after the largest 5-digit number, which is 99,999. So 99,999 + 1 = 1,00,000.
Q4. What is the largest 6-digit number?
The largest 6-digit number is 9,99,999 (nine lakh ninety-nine thousand nine hundred and ninety-nine). Adding 1 to it gives 10,00,000, which is a 7-digit number called ten lakh.
Q5. How do you place commas in the Indian number system?
Start from the right. Place the first comma after 3 digits (this separates the ones period). Then place a comma after every 2 digits. For example, the number 4567890 becomes 45,67,890 (forty-five lakh sixty-seven thousand eight hundred and ninety).
Q6. What is the difference between face value and place value?
Face value is the digit itself and never changes regardless of position (e.g., face value of 5 is always 5). Place value depends on the digit's position (e.g., 5 in the lakhs place has a place value of 5,00,000, but 5 in the tens place has a place value of 50).
Q7. How are numbers up to lakhs used in daily life?
Large numbers are used to express populations of cities (e.g., 4,50,000 people), prices of cars and houses (e.g., ₹7,50,000), bank account balances, distances between cities in metres, and student counts in large school chains.
Q8. How many 6-digit numbers are there in all?
There are exactly 9,00,000 six-digit numbers -- from 1,00,000 to 9,99,999. This is calculated as 9,99,999 - 1,00,000 + 1 = 9,00,000.
Q9. What is the relationship between lakh and thousand?
1 lakh = 100 thousands. So 5 lakhs = 5,00,000 = 500 thousands. Conversely, 50 thousands = 50,000 = half a lakh. This conversion is useful when switching between different ways of expressing large amounts.
Q10. Is 'Numbers up to Lakhs' in the NCERT Class 5 syllabus?
Yes. The NCERT Class 5 Maths textbook (Math-Magic) covers large numbers including lakhs in Chapter 1 'The Fish Tale' and related chapters. Students learn to read, write, compare, and perform operations with numbers up to lakhs as part of the CBSE curriculum.
Related Topics
- 5-Digit Numbers
- Place Value of Large Numbers
- Indian and International Number System (Grade 5)
- Reading and Writing Large Numbers
- Comparing Large Numbers (Grade 5)
- Ordering Large Numbers (Grade 5)
- Rounding Large Numbers
- Estimation (Grade 5)
- Roman Numerals (I to M)
- Numbers up to Crores
- Number Names in Lakhs and Crores
- Expanded Form of Large Numbers
