Expanded Form of 4-Digit Numbers

Class 4Large Numbers (Grade 4)

The expanded form of a number shows it as the sum of the place values of each digit. For a 4-digit number, the expanded form breaks the number into thousands + hundreds + tens + ones.

For example, 3456 in expanded form is 3000 + 400 + 50 + 6.

Writing numbers in expanded form strengthens understanding of place value and helps in performing addition, subtraction, and comparison of large numbers.

What is Expanded Form of 4-Digit Numbers - Class 4 Maths (Large Numbers)?

The expanded form of a number expresses it as the sum of the values of each digit according to its place.

Expanded Form = (Th x 1000) + (H x 100) + (T x 10) + (O x 1)

Example: The number 5,283

Digit	Place	Value
5	Thousands	5 x 1000 = 5000
2	Hundreds	2 x 100 = 200
8	Tens	8 x 10 = 80
3	Ones	3 x 1 = 3

Expanded form: 5000 + 200 + 80 + 3

There are two ways to write the expanded form:

Sum form: 5000 + 200 + 80 + 3
Multiplicative form: 5 x 1000 + 2 x 100 + 8 x 10 + 3 x 1

Types and Properties

Expanded form of numbers with zeros:

When a digit is 0, its place value is 0. You can either skip it or write it as 0.

4,036 = 4000 + 0 + 30 + 6 = 4000 + 30 + 6
7,400 = 7000 + 400 + 0 + 0 = 7000 + 400
9,005 = 9000 + 0 + 0 + 5 = 9000 + 5

Converting expanded form back to standard form:

Simply add all the values together.

6000 + 300 + 20 + 1 = 6321
2000 + 70 + 8 = 2078 (hundreds digit is 0)
8000 + 500 = 8500 (tens and ones are 0)

Solved Examples

Example 1: Example 1: Writing expanded form

Problem: Write 7,564 in expanded form.

Solution:

Step 1: Identify each digit and its place value:

7 x 1000 = 7000
5 x 100 = 500
6 x 10 = 60
4 x 1 = 4

Answer: 7564 = 7000 + 500 + 60 + 4

Example 2: Example 2: Expanded form with zeros

Problem: Write 3,008 in expanded form.

Solution:

Step 1: 3 is in thousands = 3000

Step 2: 0 is in hundreds = 0

Step 3: 0 is in tens = 0

Step 4: 8 is in ones = 8

Answer: 3008 = 3000 + 8

Example 3: Example 3: Standard form from expanded form

Problem: Write the standard form: 6000 + 200 + 50 + 3.

Solution:

Step 1: Add all values: 6000 + 200 + 50 + 3 = 6253

Answer: 6253

Example 4: Example 4: Standard form with missing places

Problem: Write the standard form: 4000 + 60 + 7.

Solution:

Step 1: 4000 — thousands digit is 4

Step 2: No hundreds value — hundreds digit is 0

Step 3: 60 — tens digit is 6

Step 4: 7 — ones digit is 7

Answer: 4067

Example 5: Example 5: Multiplicative expanded form

Problem: Write 9,241 in multiplicative expanded form.

Solution:

Answer: 9241 = 9 x 1000 + 2 x 100 + 4 x 10 + 1 x 1

Example 6: Example 6: Word problem - school strength

Problem: Aman's school has 2,750 students. Write this number in expanded form.

Solution:

Step 1: 2 thousands = 2000

Step 2: 7 hundreds = 700

Step 3: 5 tens = 50

Step 4: 0 ones = 0

Answer: 2750 = 2000 + 700 + 50

Example 7: Example 7: Finding a digit from expanded form

Problem: In the expanded form 8000 + ___ + 30 + 5 = 8435, find the missing value.

Solution:

Step 1: 8435 = 8000 + ? + 30 + 5

Step 2: ? = 8435 - 8000 - 30 - 5 = 400

Answer: The missing value is 400.

Example 8: Example 8: Comparing expanded forms

Problem: Without converting, which is greater: (5000 + 300 + 80 + 2) or (5000 + 300 + 60 + 9)?

Solution:

Step 1: Thousands are the same (5000).

Step 2: Hundreds are the same (300).

Step 3: Compare tens: 80 > 60.

Answer: 5000 + 300 + 80 + 2 > 5000 + 300 + 60 + 9 (i.e., 5382 > 5369).

Example 9: Example 9: Word problem - train numbers

Problem: Aditi's train number is 1,906. Kavi's train number is 1000 + 900 + 60. Are they on the same train?

Solution:

Step 1: Aditi's train = 1906

Step 2: Kavi's train = 1000 + 900 + 60 = 1960

Step 3: 1906 is not equal to 1960

Answer: No, they are on different trains. Aditi's is 1906 and Kavi's is 1960.

Example 10: Example 10: Building a number from clues

Problem: The expanded form of a number is 7 x 1000 + 0 x 100 + 4 x 10 + 0 x 1. What is the number?

Solution:

Step 1: 7000 + 0 + 40 + 0 = 7040

Answer: The number is 7040.

Key Points to Remember

Expanded form writes a number as the sum of the place values of its digits.
Two types: sum form (3000 + 400 + 50 + 6) and multiplicative form (3 x 1000 + 4 x 100 + 5 x 10 + 6 x 1).
When a digit is 0, its expanded value is 0 and can be skipped in the sum.
To convert expanded form back to standard form, add all the values.
If a place value (hundreds, tens, or ones) is missing in the expanded form, that digit is 0.
Expanded form is useful for understanding place value, comparing numbers, and checking addition or subtraction.

Practice Problems

Write 4,819 in expanded form.
Write 6,003 in expanded form.
Convert to standard form: 9000 + 100 + 70 + 2.
Convert to standard form: 5000 + 40.
Write 2,360 in multiplicative expanded form.
Find the missing value: 7000 + ___ + 10 + 8 = 7518.
Neha's PIN code is 4000 + 100 + 0 + 3. What is it?
Which is greater: (3000 + 900 + 40 + 5) or (3000 + 800 + 90 + 9)? Explain.

Frequently Asked Questions

Q1. What is the expanded form of a number?

The expanded form shows a number as the sum of the place values of each digit. For example, 2745 = 2000 + 700 + 40 + 5.

Q2. How do you write expanded form when there is a 0 in the number?

The place value of 0 is 0, so it can be skipped. For example, 5,030 = 5000 + 30 (the hundreds and ones are both 0).

Q3. What is the difference between expanded form and standard form?

Standard form is the normal way of writing a number (e.g., 4826). Expanded form breaks it into place values (e.g., 4000 + 800 + 20 + 6). Both represent the same number.

Q4. What is multiplicative expanded form?

It shows each digit multiplied by its place value. Example: 3572 = 3 x 1000 + 5 x 100 + 7 x 10 + 2 x 1. This form clearly shows the digit and its position.

Q5. How do you convert expanded form back to a number?

Add all the values together. If a place value is missing, put 0 in that position. For example, 6000 + 50 + 3 = 6053 (0 in hundreds place).

Q6. Can expanded form help in comparing numbers?

Yes. Compare the thousands values first, then hundreds, then tens, then ones — just like in place-value comparison. The expanded form makes each place value visible.

Q7. Is expanded form of 4-digit numbers in NCERT Class 4?

Yes. NCERT Class 4 Math Magic covers expanded form as part of the chapter on large numbers. Students learn to write numbers in expanded form and convert back to standard form.

Q8. Why is learning expanded form important?

Expanded form builds a strong understanding of place value, which is essential for addition with regrouping, subtraction with borrowing, rounding, and estimation of large numbers.

Expanded Form of 4-Digit Numbers

What is Expanded Form of 4-Digit Numbers - Class 4 Maths (Large Numbers)?

Types and Properties

Solved Examples

Example 1: Example 1: Writing expanded form

Example 2: Example 2: Expanded form with zeros

Example 3: Example 3: Standard form from expanded form

Example 4: Example 4: Standard form with missing places

Example 5: Example 5: Multiplicative expanded form

Example 6: Example 6: Word problem - school strength

Example 7: Example 7: Finding a digit from expanded form

Example 8: Example 8: Comparing expanded forms

Example 9: Example 9: Word problem - train numbers

Example 10: Example 10: Building a number from clues

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. What is the expanded form of a number?

Q2. How do you write expanded form when there is a 0 in the number?

Q3. What is the difference between expanded form and standard form?

Q4. What is multiplicative expanded form?

Q5. How do you convert expanded form back to a number?

Q6. Can expanded form help in comparing numbers?

Q7. Is expanded form of 4-digit numbers in NCERT Class 4?

Q8. Why is learning expanded form important?

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