Learning Objectives
- Understand place value of digits in numbers up to 5 digits (ten thousands).
- Learn the Indian number system: Ones, Tens, Hundreds, Thousands, Ten Thousands.
- Write the expanded form of 5-digit numbers.
- Know the difference between face value and place value.
- Compare 4-digit and 5-digit numbers using > and <.
- Arrange numbers in ascending and descending order.
- Form the greatest and smallest numbers from given digits.
Let Us Begin!
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.
The Indian Number System -- Place Value Chart
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:
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.
[Image: Value of a Digit Depends on its Place — the digit 5 in ones place (=5), tens place (=50), hundreds place (=500), thousands place (=5000). Visual blocks/stacks showing the difference.]
Expanded Form of 5-Digit Numbers
The expanded form shows the value of each digit based on its place.
Example 1: Write the expanded form of 36,185
36,185 = 30,000 + 6,000 + 100 + 80 + 5
Or: 3 × 10,000 + 6 × 1,000 + 1 × 100 + 8 × 10 + 5 × 1
Example 2: Write the expanded form of 50,407
50,407 = 50,000 + 0 + 400 + 0 + 7
Or: 5 × 10,000 + 0 × 1,000 + 4 × 100 + 0 × 10 + 7 × 1
Think about it: What is the expanded form of 82,916?
Face Value vs Place Value
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.
Example 3: Find the face value and place value of each digit in 63,472
| 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.
Comparing Numbers
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.
Example 4: Compare 45,678 and 45,312
Both are 5-digit numbers. TT digit: 4 = 4. Th digit: 5 = 5. H digit: 6 > 3. So 45,678 > 45,312.
Key Words and Meanings
| 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 and Descending Order
Ascending order means arranging numbers from the smallest to the greatest.
Descending order means arranging numbers from the greatest to the smallest.
Example 5: Arrange in ascending order: 34,210; 8,765; 34,021; 52,100
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
Example 6: Arrange in descending order: 71,450; 17,540; 71,054; 75,410
Descending: 75,410 > 71,450 > 71,054 > 17,540
Forming Greatest and Smallest Numbers
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.
Example 7: Form the greatest and smallest 5-digit numbers using digits 7, 2, 9, 4, 1
Greatest: Arrange in descending order: 97,421
Smallest: Arrange in ascending order: 12,479
Example 8: Form the greatest and smallest 5-digit numbers using digits 5, 0, 3, 8, 0
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?
⭐ Key Points to Remember
- In the Indian system, places are: Ones, Tens, Hundreds, Thousands, Ten Thousands.
- Expanded form shows the value of each digit: 47,253 = 40,000 + 7,000 + 200 + 50 + 3.
- Face value is the digit itself. Place value depends on the digit's position.
- A 5-digit number is always greater than a 4-digit number.
- To compare numbers with the same digits, start from the leftmost digit.
- For the greatest number, arrange digits in descending order.
- For the smallest number, arrange digits in ascending order (0 cannot be first).
Practice Questions
A. Fill in the Blanks
1. The place value of 6 in 26,345 is .
2. The face value of 8 in 58,012 is .
3. The expanded form of 41,506 is .
4. The smallest 5-digit number is .
5. The greatest 4-digit number is .
B. Compare Using > or <
1. 32,456 32,465
2. 9,999 10,000
3. 78,123 77,999
4. 50,050 50,500
C. Multiple Choice Questions
1. The place value of 3 in 73,841 is:
(a) 3(b) 300(c) 3,000(d) 30,000
2. Which is the greatest number?
(a) 89,321(b) 98,321(c) 89,231(d) 93,821
3. The smallest 5-digit number formed using 4, 0, 7, 2, 0 is:
(a) 00,247(b) 20,047(c) 20,074(d) 24,007
D. Write the Expanded Form
1. 29,374 =
2. 60,508 =
E. Arrange in Order
1. Ascending order: 45,320; 9,876; 45,230; 54,320
2. Descending order: 23,456; 32,654; 23,654; 32,456
F. Form the Greatest and Smallest Numbers
1. Using digits 3, 8, 1, 5, 6: Greatest = Smallest =
2. Using digits 9, 0, 2, 7, 0: Greatest = Smallest =
🎨 Fun Activity -- Number Detective
Read the clues and find the mystery 5-digit number:
- The digit in the ten thousands place is 6.
- The digit in the ones place is half of 8.
- The digit in the hundreds place is 0.
- The digit in the thousands place is 3 more than the ones digit.
- The digit in the tens place is the same as the ten thousands digit.
The mystery number is:
Write its expanded form:
Write it in words: