Place Value of 4-Digit Numbers
Every digit in a number has a place value based on its position. In a 4-digit number, the four places from left to right are Thousands (Th), Hundreds (H), Tens (T), and Ones (O).
Understanding place value helps you read, write, compare, and perform operations on 4-digit numbers correctly. It is the foundation of our decimal number system (base-10 system), where each place is 10 times the place to its right.
What is Place Value of 4-Digit Numbers - Class 4 Maths (Large Numbers)?
Place value is the value of a digit based on its position in a number. It is different from the face value (the digit itself).
| Term | Meaning | Example (digit 5 in 5,283) |
|---|---|---|
| Face Value | The digit itself | 5 |
| Place Value | Face value x value of the position | 5 x 1000 = 5000 |
Place Value Chart for 4-Digit Numbers:
| Place | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|---|
| Value | 1000 | 100 | 10 | 1 |
Each place is 10 times the place to its right: 1000 = 10 x 100, 100 = 10 x 10, 10 = 10 x 1.
Place Value of 4-Digit Numbers Formula
Place Value of a Digit = Face Value x Value of its Position
Position values in a 4-digit number:
- Thousands place = x 1000
- Hundreds place = x 100
- Tens place = x 10
- Ones place = x 1
Types and Properties
How to find place value of each digit:
Consider the number 6,394:
| Digit | Position | Place Value |
|---|---|---|
| 6 | Thousands | 6 x 1000 = 6000 |
| 3 | Hundreds | 3 x 100 = 300 |
| 9 | Tens | 9 x 10 = 90 |
| 4 | Ones | 4 x 1 = 4 |
Verification: 6000 + 300 + 90 + 4 = 6394
Place value of 0:
The digit 0 in any place has a place value of 0. In the number 3056, the digit 0 is in the hundreds place. Its place value = 0 x 100 = 0. However, 0 acts as a placeholder — without it, the number changes (356 is not 3056).
Solved Examples
Example 1: Example 1: Writing place values of all digits
Problem: Write the place value of each digit in 4,827.
Solution:
| Digit | Place | Place Value |
|---|---|---|
| 4 | Thousands | 4000 |
| 8 | Hundreds | 800 |
| 2 | Tens | 20 |
| 7 | Ones | 7 |
Answer: Place values are 4000, 800, 20, and 7.
Example 2: Example 2: Place value vs face value
Problem: What is the place value and face value of 3 in 1,362?
Solution:
Step 1: Locate 3 in 1,362 — it is in the hundreds place.
Step 2: Face value of 3 = 3
Step 3: Place value of 3 = 3 x 100 = 300
Answer: Face value = 3, Place value = 300
Example 3: Example 3: Place value of 0
Problem: What is the place value of 0 in 7,089?
Solution:
Step 1: In 7,089 — 7 is in thousands, 0 is in hundreds, 8 is in tens, 9 is in ones.
Step 2: Place value of 0 = 0 x 100 = 0
Answer: The place value of 0 in 7,089 is 0. It is a placeholder that keeps other digits in their correct positions.
Example 4: Example 4: Finding the number from place values
Problem: A number has place values 5000, 200, 40, and 6. What is the number?
Solution:
Step 1: Add all place values: 5000 + 200 + 40 + 6 = 5246
Answer: The number is 5246.
Example 5: Example 5: Comparing place values of the same digit
Problem: In the number 3,535, the digit 5 appears twice. Find the place value of each 5.
Solution:
| Position | Th | H | T | O |
|---|---|---|---|---|
| Digit | 3 | 5 | 3 | 5 |
Step 1: First 5 is in the hundreds place: 5 x 100 = 500
Step 2: Second 5 is in the ones place: 5 x 1 = 5
Step 3: The hundreds-place 5 is 500 / 5 = 100 times the ones-place 5.
Answer: Place values are 500 and 5. The hundreds 5 is 100 times the ones 5.
Example 6: Example 6: Word problem - savings
Problem: Meera's father saved ₹8,465 in a month. What is the place value of 4 in this amount?
Solution:
Step 1: In ₹8,465 — 8 is in thousands, 4 is in hundreds.
Step 2: Place value of 4 = 4 x 100 = 400
Answer: The place value of 4 in ₹8,465 is ₹400.
Example 7: Example 7: Mystery number puzzle
Problem: I am a 4-digit number. My thousands digit has a place value of 2000. My hundreds digit has a place value of 600. My tens digit is 0. My ones digit is 9. What number am I?
Solution:
Step 1: Thousands digit: 2000 / 1000 = 2
Step 2: Hundreds digit: 600 / 100 = 6
Step 3: Tens digit: 0
Step 4: Ones digit: 9
Answer: The number is 2609.
Example 8: Example 8: Relationship between places
Problem: How many times is the value of the thousands place compared to the ones place?
Solution:
Step 1: Thousands place value = 1000
Step 2: Ones place value = 1
Step 3: 1000 / 1 = 1000
Answer: The thousands place is 1000 times the ones place.
Example 9: Example 9: Word problem - distance
Problem: The distance from Ria's house to her grandparents' village is 1,473 km. What is the sum of the place values of all the digits?
Solution:
Step 1: Place value of 1 = 1000
Step 2: Place value of 4 = 400
Step 3: Place value of 7 = 70
Step 4: Place value of 3 = 3
Step 5: Sum = 1000 + 400 + 70 + 3 = 1473
Answer: The sum of place values = 1473 (this always equals the number itself).
Example 10: Example 10: Finding the difference of place values
Problem: Find the difference between the place values of the two 6s in 6,164.
Solution:
Step 1: First 6 (from left) is in the thousands place: 6 x 1000 = 6000
Step 2: Second 6 is in the tens place: 6 x 10 = 60
Step 3: Difference = 6000 - 60 = 5940
Answer: The difference of place values = 5940.
Key Points to Remember
- Place value = face value x value of the position.
- In a 4-digit number, the places are: Thousands (1000), Hundreds (100), Tens (10), Ones (1).
- Each place is 10 times the place to its right.
- The face value of a digit never changes; the place value changes with position.
- The place value of 0 is always 0, but 0 is essential as a placeholder.
- The sum of place values of all digits in a number equals the number itself.
- Same digit in different places has different place values (e.g., 5 in hundreds = 500, 5 in ones = 5).
Practice Problems
- Write the place value of each digit in 9,304.
- What is the place value of 7 in 7,150?
- In 4,848, find the place value of each 8. How many times greater is the larger place value?
- A number has place values 3000, 0, 50, and 1. What is the number?
- Find the difference between the place values of 2 in 2,324.
- Dev's school has 1,206 students. What is the place value of 2 in this number?
- I am a 4-digit number. My thousands digit has place value 9000. My hundreds digit has place value 100. My tens and ones digits are both 0. What number am I?
- True or false: The place value of 5 is always 500. Explain.
Frequently Asked Questions
Q1. What is place value?
Place value is the value of a digit based on its position in a number. The same digit has different values in different positions. For example, 3 in the thousands place = 3000, but 3 in the tens place = 30.
Q2. What is the difference between place value and face value?
Face value is the digit itself and never changes. Place value depends on position. In 4,582, the face value of 5 is 5, but its place value is 500 (because it is in the hundreds place).
Q3. What is the place value of 0?
The place value of 0 is always 0, regardless of its position. However, 0 is crucial as a placeholder. Without it, 3056 would become 356 — a completely different number.
Q4. Why is the place value system called base-10?
Because each place is 10 times the value of the place to its right. Ones x 10 = Tens, Tens x 10 = Hundreds, Hundreds x 10 = Thousands. This is why it is also called the decimal system.
Q5. How many places does a 4-digit number have?
Four places: Thousands (Th), Hundreds (H), Tens (T), and Ones (O), reading from left to right.
Q6. Can a digit have the same face value and place value?
Yes, but only in the ones place. A digit in the ones position has place value = digit x 1, which equals the digit itself (its face value). In all other positions, the place value is larger.
Q7. What is the sum of place values of all digits in a number?
The sum of place values of all digits always equals the number itself. For example, in 2753: 2000 + 700 + 50 + 3 = 2753.
Q8. How is place value useful in real life?
Place value helps you read prices (₹4,590), distances (1,250 km), populations, and PIN codes correctly. It is also essential for performing addition, subtraction, and other operations with large numbers.
Q9. Is place value of 4-digit numbers in the NCERT Class 4 syllabus?
Yes. The NCERT Class 4 Maths textbook (Math Magic) covers place value of 4-digit and 5-digit numbers, including expanded form and comparing numbers using place value.
Related Topics
- 4-Digit Numbers
- Expanded Form of 4-Digit Numbers
- 5-Digit Numbers
- Place Value of 5-Digit Numbers
- Comparing Large Numbers (Grade 4)
- Ordering Large Numbers (Grade 4)
- Rounding Numbers (Grade 4)
- Estimation (Grade 4)
- Roman Numerals (I to C)
- Numbers up to 1,00,000
- Predecessor and Successor (Grade 4)
- Number Names for Large Numbers
