Numbers up to 1,00,000
Numbers up to 1,00,000 (one lakh) form the foundation of the Indian number system studied in Class 4. In earlier classes, you worked with numbers up to 9,999. Now you will extend your understanding to 5-digit and 6-digit numbers that go all the way up to 99,999 and then to 1,00,000.
Large numbers appear everywhere in daily life. A car may cost ₹5,50,000, a school may have 12,500 students, or a city's population may be 98,000. Understanding how to read, write, and compare these numbers is essential for real-life calculations.
What is Numbers up to 1,00,000 - Class 4 Maths (Large Numbers)?
A 5-digit number has digits in five places: Ten-Thousands, Thousands, Hundreds, Tens, and Ones. The smallest 5-digit number is 10,000 (ten thousand) and the largest is 99,999 (ninety-nine thousand nine hundred and ninety-nine).
The number 1,00,000 is called one lakh in the Indian system. It is the smallest 6-digit number and comes right after 99,999.
In the Indian place value system, we use commas after the thousands place and then after every two digits. For example: 1,00,000 or 56,789 or 1,23,456.
Numbers up to 1,00,000 Formula
Indian Place Value Chart (up to 1,00,000)
| Lakhs (L) | Ten-Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|---|---|
| 1,00,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Expanded form: Any number can be written as the sum of the value of each digit.
Example: 45,382 = 40,000 + 5,000 + 300 + 80 + 2
Types and Properties
Types of large numbers covered in Class 4:
- 5-digit numbers: From 10,000 to 99,999. Example: 23,456 (Twenty-three thousand four hundred and fifty-six).
- The number 1,00,000: One lakh — the smallest 6-digit number.
Indian vs International system:
| Number | Indian System | International System |
|---|---|---|
| 50,000 | Fifty thousand | Fifty thousand |
| 1,00,000 | One lakh | One hundred thousand |
Solved Examples
Example 1: Example 1: Writing a Number in Expanded Form
Problem: Write 63,547 in expanded form.
Solution:
Step 1: Identify the place value of each digit.
6 is in the ten-thousands place → 60,000
3 is in the thousands place → 3,000
5 is in the hundreds place → 500
4 is in the tens place → 40
7 is in the ones place → 7
Step 2: Write as a sum.
Answer: 63,547 = 60,000 + 3,000 + 500 + 40 + 7
Example 2: Example 2: Finding the Place Value of a Digit
Problem: What is the place value of 8 in 48,215?
Solution:
Step 1: Locate digit 8 in the number 48,215.
The digit 8 is in the thousands place.
Step 2: Multiply the digit by its place value.
8 × 1,000 = 8,000
Answer: The place value of 8 in 48,215 is 8,000.
Example 3: Example 3: Writing Number Names
Problem: Write the number name for 75,309.
Solution:
Step 1: Break the number using place values.
75,309 = 75 thousands + 3 hundreds + 0 tens + 9 ones
Step 2: Write in words.
Answer: Seventy-five thousand three hundred and nine
Example 4: Example 4: Writing Numerals from Number Names
Problem: Write the numeral for "Forty-six thousand two hundred and eighteen."
Solution:
Step 1: Forty-six thousand = 46,000
Step 2: Two hundred and eighteen = 218
Step 3: Add: 46,000 + 218 = 46,218
Answer: 46,218
Example 5: Example 5: Comparing 5-digit Numbers
Problem: Which is greater: 58,432 or 58,491?
Solution:
Step 1: Both numbers have the same ten-thousands digit (5) and thousands digit (8).
Step 2: Compare the hundreds digit: 4 = 4 (same).
Step 3: Compare the tens digit: 3 < 9.
Answer: 58,491 > 58,432
Example 6: Example 6: Successor of a Large Number
Problem: What comes just after 99,999?
Solution:
Step 1: The successor is found by adding 1.
99,999 + 1 = 1,00,000
Answer: The successor of 99,999 is 1,00,000 (one lakh).
Example 7: Example 7: Ordering Numbers
Problem: Arrange in ascending order: 34,500; 34,050; 34,005; 35,400.
Solution:
Step 1: Compare the ten-thousands and thousands digits first. All start with 3, then check the next digits.
Step 2: 34,005 < 34,050 < 34,500 < 35,400
Answer: 34,005 < 34,050 < 34,500 < 35,400
Example 8: Example 8: Word Problem on Large Numbers
Problem: Aman's school has 12,450 students. Priya's school has 13,280 students. How many students do both schools have in total?
Solution:
Step 1: Add the two numbers.
12,450 + 13,280 = 25,730
Answer: Both schools have 25,730 students in total.
Example 9: Example 9: Building a Number from Clues
Problem: A 5-digit number has 4 in the ten-thousands place, 0 in the thousands place, 7 in the hundreds place, 3 in the tens place, and 9 in the ones place. What is the number?
Solution:
Step 1: Write each digit in its correct place.
| TTh | Th | H | T | O |
|---|---|---|---|---|
| 4 | 0 | 7 | 3 | 9 |
Answer: The number is 40,739.
Example 10: Example 10: Finding the Difference
Problem: Rahul's father earned ₹78,500 in January and ₹65,200 in February. How much more did he earn in January?
Solution:
Step 1: Subtract to find the difference.
78,500 − 65,200 = 13,300
Answer: Rahul's father earned ₹13,300 more in January.
Real-World Applications
Where do we use numbers up to 1,00,000?
- Population: A town may have a population of 85,000 people.
- Money: A motorcycle costs ₹72,500; a holiday trip costs ₹45,000.
- Distance: The distance between two cities may be 15,000 km.
- Sports: A cricket stadium holds 50,000 spectators.
- School data: Total marks of all students in a school can go up to thousands.
Key Points to Remember
- The smallest 5-digit number is 10,000 and the largest is 99,999.
- 1,00,000 (one lakh) is the smallest 6-digit number.
- In the Indian system, commas are placed after the thousands place and then after every two digits (e.g., 1,23,456).
- Each place value is 10 times the place value to its right.
- To compare numbers, start from the leftmost digit and move right.
- Expanded form shows the value of each digit separately.
- The face value of a digit is the digit itself; the place value depends on its position.
Practice Problems
- Write 82,046 in expanded form.
- What is the place value of 5 in 50,731?
- Write the number name for 91,605.
- Arrange in descending order: 45,600; 46,500; 45,060; 44,650.
- Meera saved ₹23,500 in the first year and ₹31,200 in the second year. How much did she save in total?
- What number is 1 more than 49,999?
- Write the numeral: Sixty-seven thousand eight hundred and twelve.
- A 5-digit number has 9 in the ten-thousands place, 0 in the thousands place, 5 in the hundreds place, 8 in the tens place, and 1 in the ones place. What is the number?
Frequently Asked Questions
Q1. What is the largest 5-digit number?
The largest 5-digit number is 99,999 (ninety-nine thousand nine hundred and ninety-nine). Adding 1 to it gives 1,00,000, which is a 6-digit number.
Q2. How do you read 1,00,000 in the Indian system?
1,00,000 is read as "one lakh" in the Indian number system. In the international system, it is read as "one hundred thousand."
Q3. What is the difference between face value and place value?
The face value of a digit is the digit itself regardless of its position. The place value depends on the position. For example, in 47,230, the face value of 4 is 4, but its place value is 40,000.
Q4. How do you write 5-digit numbers using commas in the Indian system?
In the Indian system, place a comma after the thousands digit. For example, 56789 is written as 56,789. For 6-digit numbers, an additional comma appears after the lakhs digit: 1,23,456.
Q5. How do you compare two 5-digit numbers?
Start comparing from the leftmost digit (ten-thousands place). If those digits are the same, move to the thousands digit, then hundreds, tens, and ones. The number with the first larger digit at any place is the greater number.
Q6. What is the expanded form of a number?
Expanded form breaks a number into the sum of the value of each digit. For example, 36,482 = 30,000 + 6,000 + 400 + 80 + 2.
Q7. How many 5-digit numbers are there in all?
There are 90,000 five-digit numbers in total (from 10,000 to 99,999). This is calculated as 99,999 − 10,000 + 1 = 90,000.
Q8. What comes just before 1,00,000?
The number just before 1,00,000 is 99,999. It is the predecessor of 1,00,000 and the largest 5-digit number.
Q9. Is numbers up to 1,00,000 part of the NCERT Class 4 syllabus?
Yes, understanding numbers up to 1,00,000 is part of the CBSE/NCERT curriculum for Class 4 under the chapter on large numbers. Students learn to read, write, compare, and order these numbers.
Related Topics
- 5-Digit Numbers
- Place Value of 5-Digit Numbers
- 4-Digit Numbers
- Place Value of 4-Digit Numbers
- Expanded Form of 4-Digit Numbers
- Comparing Large Numbers (Grade 4)
- Ordering Large Numbers (Grade 4)
- Rounding Numbers (Grade 4)
- Estimation (Grade 4)
- Roman Numerals (I to C)
- Predecessor and Successor (Grade 4)
- Number Names for Large Numbers
