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.
| 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:
| L | T-Th | Th | H | T | O |
|---|---|---|---|---|---|
| 5 | 2 | 3 | 4 | 6 | 8 |
We read this as: Five lakh twenty-three thousand four hundred sixty-eight.
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 shows the value of each digit based on its place.
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
72,415 = Seventy-two thousand four hundred fifteen
1,08,030 = One lakh eight thousand thirty
6,50,009 = Six lakh fifty thousand nine
| 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 |
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.
Both are 6-digit numbers. Lakhs digit: both are 4 (same). Ten-thousands digit: 5 > 4. So, 4,52,318 > 4,48,926.
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.
A. Write the number names.
B. Write in figures (numerals).
C. Write in expanded form.
D. Place commas according to the Indian system.
E. Compare using >, <, or =.
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?
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: _________________ < _________________ < _________________