Learning Objectives
- Read and write numbers up to 6 digits (up to 9,99,999).
- Understand the Indian number system and place commas correctly.
- Know the place value of each digit up to the Lakhs place.
- Write number names for 5-digit and 6-digit numbers.
- Write numbers in expanded form.
- Compare large numbers and find predecessor and successor.
Let Us Begin!
You already know numbers up to 9,999 (four digits). Now let us learn about bigger numbers!
The population of a small town might be 45,230 (a 5-digit number). The price of a car might be 7,85,000 (a 6-digit number). These are large numbers.
In the Indian number system, we place commas to make large numbers easy to read. The first comma comes after the thousands place (after 3 digits from the right), and the next comma comes after every 2 digits after that.
Place Value Chart (Indian System)
| Lakhs (L) | Ten-Thousands (T-Th) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
| 1,00,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Reading the number 5,23,468:
We read this as: Five lakh twenty-three thousand four hundred sixty-eight.
[Image: Indian Number System — Place Value Chart showing columns Lakhs, Ten-Thousands, Thousands, Hundreds, Tens, Ones with the number 5,23,468 placed in it and commas marked]
Placing Commas in the Indian System
Rule: Start from the right. Place the first comma after 3 digits. Then place a comma after every 2 digits.
Number: 123456 → With commas: 1,23,456 (One lakh twenty-three thousand four hundred fifty-six)
Number: 999999 → With commas: 9,99,999 (Nine lakh ninety-nine thousand nine hundred ninety-nine)
Number: 50307 → With commas: 50,307 (Fifty thousand three hundred seven)
Think: The largest 6-digit number is 9,99,999. The smallest 6-digit number is 1,00,000 (one lakh).
Expanded Form
Expanded form shows the value of each digit based on its place.
Example: Write 3,45,672 in expanded form
3,45,672 = 3,00,000 + 40,000 + 5,000 + 600 + 70 + 2
= 3 Lakhs + 4 Ten-Thousands + 5 Thousands + 6 Hundreds + 7 Tens + 2 Ones
Number Names
Examples:
72,415 = Seventy-two thousand four hundred fifteen
1,08,030 = One lakh eight thousand thirty
6,50,009 = Six lakh fifty thousand nine
Comparing Large Numbers
Rule 1: A number with more digits is always greater. (6-digit > 5-digit)
Rule 2: If both numbers have the same number of digits, compare from the leftmost digit.
Example: Compare 4,52,318 and 4,48,926
Both are 6-digit numbers. Lakhs digit: both are 4 (same). Ten-thousands digit: 5 > 4. So, 4,52,318 > 4,48,926.
Predecessor and Successor
Predecessor = number − 1. Successor = number + 1.
Predecessor of 3,00,000 is 2,99,999. Successor of 3,00,000 is 3,00,001.
Predecessor of 1,00,000 is 99,999. Successor of 9,99,999 is 10,00,000.
Key Words
| Word | Meaning |
|---|
| Place Value | The value of a digit based on its position in the number |
| Lakh | 1,00,000 (one hundred thousand in the Indian system) |
| Expanded Form | Writing a number as the sum of the values of each digit |
| Predecessor | The number that comes just before a given number (1 less) |
| Successor | The number that comes just after a given number (1 more) |
| Indian Number System | A system of placing commas after thousands, then every two digits |
⭐ Key Points to Remember:
- In the Indian system, commas are placed after the first 3 digits from the right, then after every 2 digits.
- The place values (right to left) are: Ones, Tens, Hundreds, Thousands, Ten-Thousands, Lakhs.
- The smallest 5-digit number is 10,000. The largest is 99,999.
- The smallest 6-digit number is 1,00,000 (one lakh). The largest is 9,99,999.
- To compare numbers with the same number of digits, start from the leftmost digit.
- Predecessor = 1 less. Successor = 1 more.
Practice Questions
A. Write the number names.
1. 85,214 =
2. 3,07,560 =
3. 9,10,005 =
B. Write in figures (numerals).
1. Two lakh thirty-five thousand one hundred twelve =
2. Seven lakh nine thousand forty =
3. Sixty thousand eight hundred one =
C. Write in expanded form.
1. 4,62,815 =
2. 7,05,030 =
D. Place commas according to the Indian system.
1. 308472 =
2. 750016 =
3. 99999 =
E. Compare using >, <, or =.
1. 5,43,210 5,34,210
2. 99,999 1,00,000
3. 8,08,080 8,08,008
F. Write the predecessor and successor.
| Predecessor | Number | Successor |
|---|
| 4,00,000 | |
| 99,999 | |
| 7,50,100 | |
| 1,00,000 | |
G. What is the place value of the underlined digit?
1. In 6,34,521, the place value of 3 is
2. In 8,12,407, the place value of 8 is
3. In 2,50,613, the place value of 6 is
🎨 Think and Do — Fun Activity:
Number Hunt: Look at newspapers, magazines, or advertisements at home. Find 3 large numbers (5-digit or 6-digit). Write them below with their number names.
1. Number: _________________ Name: ___________________________________
2. Number: _________________ Name: ___________________________________
3. Number: _________________ Name: ___________________________________
Now arrange your 3 numbers from smallest to greatest: _________________ < _________________ < _________________