In Class 3, you learned about numbers up to 4 digits (up to 9,999). Now in Class 4, we will work with 5-digit numbers -- numbers up to 99,999! The population of a small town, the price of a television, or the distance between two cities in kilometres -- all of these use 5-digit numbers.
Understanding place value helps us read, write, and compare big numbers correctly. Let us explore how each digit in a number has a special value based on its position.
In Class 3, you learned about numbers up to 4 digits (up to 9,999). Now in Class 4, we will work with 5-digit numbers -- numbers up to 99,999! The population of a small town, the price of a television, or the distance between two cities in kilometres -- all of these use 5-digit numbers.
Understanding place value helps us read, write, and compare big numbers correctly. Let us explore how each digit in a number has a special value based on its position.
In the Indian number system, the places from right to left are:
| Ten Thousands (TT) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|---|
| 10,000 | 1,000 | 100 | 10 | 1 |
Let us place the number 47,253 in the chart:
| TT | Th | H | T | O |
|---|---|---|---|---|
| 4 | 7 | 2 | 5 | 3 |
We read this number as: Forty-seven thousand two hundred and fifty-three.
In the Indian system, we put a comma after the thousands place: 47,253.
The expanded form shows the value of each digit based on its place.
36,185 = 30,000 + 6,000 + 100 + 80 + 5
Or: 3 x 10,000 + 6 x 1,000 + 1 x 100 + 8 x 10 + 5 x 1
50,407 = 50,000 + 0 + 400 + 0 + 7
Or: 5 x 10,000 + 0 x 1,000 + 4 x 100 + 0 x 10 + 7 x 1
Every digit in a number has two values:
Face Value: The digit itself, no matter where it is placed. The face value of 5 is always 5.
Place Value: The value of the digit based on its position in the number.
| Digit | Place | Face Value | Place Value |
|---|---|---|---|
| 6 | Ten Thousands | 6 | 60,000 |
| 3 | Thousands | 3 | 3,000 |
| 4 | Hundreds | 4 | 400 |
| 7 | Tens | 7 | 70 |
| 2 | Ones | 2 | 2 |
Remember: The face value of 0 is always 0, and the place value of 0 is also always 0, no matter where it is placed.
Rule 1: A number with more digits is always greater. A 5-digit number is always greater than a 4-digit number.
Example: 10,000 > 9,999
Rule 2: If two numbers have the same number of digits, compare from the leftmost digit. The number with the greater digit at the first different place is greater.
Both are 5-digit numbers. TT digit: 4 = 4. Th digit: 5 = 5. H digit: 6 > 3. So 45,678 > 45,312.
Ascending order means arranging numbers from the smallest to the greatest.
Descending order means arranging numbers from the greatest to the smallest.
First, 8,765 is a 4-digit number (smallest). Among the 5-digit numbers, compare: 34,021 < 34,210 < 52,100.
Ascending: 8,765 < 34,021 < 34,210 < 52,100
Descending: 75,410 > 71,450 > 71,054 > 17,540
To form the greatest number: Arrange the given digits in descending order (largest digit first).
To form the smallest number: Arrange the given digits in ascending order (smallest digit first). If 0 is one of the digits, it cannot come first -- place it in the second position.
Greatest: Arrange in descending order: 97,421
Smallest: Arrange in ascending order: 12,479
Greatest: 85,300
Smallest: 30,058 (0 cannot be the first digit, so 3 comes first)
| Word | Meaning |
|---|---|
| Place value | The value of a digit based on its position in a number |
| Face value | The digit itself, regardless of its position |
| Expanded form | Writing a number as the sum of the values of each digit |
| Ascending order | Arranging numbers from smallest to greatest |
| Descending order | Arranging numbers from greatest to smallest |
Read the clues and find the mystery 5-digit number:
The mystery number is:
Write its expanded form:
Write it in words:
Want to use this as a worksheet? Switch to the A4 printable view.
In Class 3, you learned about numbers up to 4 digits (up to 9,999). Now in Class 4, we will work with 5-digit numbers -- numbers up to 99,999! The population of a small town, the price of a television, or the distance between two cities in kilometres -- all of these use 5-digit numbers.
Understanding place value helps us read, write, and compare big numbers correctly. Let us explore how each digit in a number has a special value based on its position.
In the Indian number system, the places from right to left are:
| Ten Thousands (TT) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|---|
| 10,000 | 1,000 | 100 | 10 | 1 |
Let us place the number 47,253 in the chart:
| TT | Th | H | T | O |
|---|---|---|---|---|
| 4 | 7 | 2 | 5 | 3 |
We read this number as: Forty-seven thousand two hundred and fifty-three.
In the Indian system, we put a comma after the thousands place: 47,253.
The expanded form shows the value of each digit based on its place.
36,185 = 30,000 + 6,000 + 100 + 80 + 5
Or: 3 x 10,000 + 6 x 1,000 + 1 x 100 + 8 x 10 + 5 x 1
50,407 = 50,000 + 0 + 400 + 0 + 7
Or: 5 x 10,000 + 0 x 1,000 + 4 x 100 + 0 x 10 + 7 x 1
Think about it: What is the expanded form of 82,916?
Every digit in a number has two values:
Face Value: The digit itself, no matter where it is placed. The face value of 5 is always 5.
Place Value: The value of the digit based on its position in the number.
| Digit | Place | Face Value | Place Value |
|---|---|---|---|
| 6 | Ten Thousands | 6 | 60,000 |
| 3 | Thousands | 3 | 3,000 |
| 4 | Hundreds | 4 | 400 |
| 7 | Tens | 7 | 70 |
| 2 | Ones | 2 | 2 |
Remember: The face value of 0 is always 0, and the place value of 0 is also always 0, no matter where it is placed.
Rule 1: A number with more digits is always greater. A 5-digit number is always greater than a 4-digit number.
Example: 10,000 > 9,999
Rule 2: If two numbers have the same number of digits, compare from the leftmost digit. The number with the greater digit at the first different place is greater.
Both are 5-digit numbers. TT digit: 4 = 4. Th digit: 5 = 5. H digit: 6 > 3. So 45,678 > 45,312.
| Word | Meaning |
|---|---|
| Place value | The value of a digit based on its position in a number |
| Face value | The digit itself, regardless of its position |
| Expanded form | Writing a number as the sum of the values of each digit |
| Ascending order | Arranging numbers from smallest to greatest |
| Descending order | Arranging numbers from greatest to smallest |
Ascending order means arranging numbers from the smallest to the greatest.
Descending order means arranging numbers from the greatest to the smallest.
First, 8,765 is a 4-digit number (smallest). Among the 5-digit numbers, compare: 34,021 < 34,210 < 52,100.
Ascending: 8,765 < 34,021 < 34,210 < 52,100
Descending: 75,410 > 71,450 > 71,054 > 17,540
To form the greatest number: Arrange the given digits in descending order (largest digit first).
To form the smallest number: Arrange the given digits in ascending order (smallest digit first). If 0 is one of the digits, it cannot come first -- place it in the second position.
Greatest: Arrange in descending order: 97,421
Smallest: Arrange in ascending order: 12,479
Greatest: 85,300
Smallest: 30,058 (0 cannot be the first digit, so 3 comes first)
Think about it: Using the digits 6, 1, 0, 4, 9, what is the greatest number you can form? What is the smallest?
A. Fill in the Blanks
B. Compare Using > or <
C. Multiple Choice Questions
D. Write the Expanded Form
E. Arrange in Order
F. Form the Greatest and Smallest Numbers
Read the clues and find the mystery 5-digit number:
The mystery number is:
Write its expanded form:
Write it in words: