Maths

Place Value

Class 4

🎯 Learning Objectives

📖 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.

A Friendly Introduction

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)
10,0001,000100101

Let us place the number 47,253 in the chart:

TTThHTO
47253

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.

Expanded Form of 5-Digit Numbers

The expanded form shows the value of each digit based on its place.

Example
Example 1: Write the expanded form of 36,185

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

Example
Example 2: Write the expanded form of 50,407

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?

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
Example 3: Find the face value and place value of each digit in 63,472
DigitPlaceFace ValuePlace Value
6Ten Thousands660,000
3Thousands33,000
4Hundreds4400
7Tens770
2Ones22

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
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.

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
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
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
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
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 Words

WordMeaning
Place valueThe value of a digit based on its position in a number
Face valueThe digit itself, regardless of its position
Expanded formWriting a number as the sum of the values of each digit
Ascending orderArranging numbers from smallest to greatest
Descending orderArranging numbers from greatest to smallest
⭐ Key Points to Remember

✏️ 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 mystery number is:

Write its expanded form:

Write it in words:

Want to use this as a worksheet? Switch to the A4 printable view.

Learning Objectives
A Friendly Introduction

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)
10,0001,000100101

Let us place the number 47,253 in the chart:

TTThHTO
47253

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.

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 x 10,000 + 6 x 1,000 + 1 x 100 + 8 x 10 + 5 x 1

Example 2: Write the expanded form of 50,407

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?

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
DigitPlaceFace ValuePlace Value
6Ten Thousands660,000
3Thousands33,000
4Hundreds4400
7Tens770
2Ones22

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
WordMeaning
Place valueThe value of a digit based on its position in a number
Face valueThe digit itself, regardless of its position
Expanded formWriting a number as the sum of the values of each digit
Ascending orderArranging numbers from smallest to greatest
Descending orderArranging 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
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 mystery number is:

Write its expanded form:

Write it in words: