Solved Exercises on Number in Expanded Form Examples in Grade 4

Master number in expanded form examples: place value decomposition, digit representation, and number composition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic expanded form example
Exercise 1
Write the number 4,728 in expanded form.
Definition:

Expanded form: Writing a number to show the value of each digit based on its place value.

Expanded Form Method:
  1. Identify the place value of each digit
  2. Write each digit multiplied by its place value
  3. Join all parts with addition signs
Number
4,728
Expanded Form
4,000 + 700 + 20 + 8
Step 1: Identify place values

4 is in thousands place: 4 × 1,000 = 4,000

7 is in hundreds place: 7 × 100 = 700

2 is in tens place: 2 × 10 = 20

8 is in ones place: 8 × 1 = 8

Step 2: Write in expanded form

4,728 = 4,000 + 700 + 20 + 8

Step 3: Verify the calculation

4,000 + 700 + 20 + 8 = 4,728 ✓

4,728 = 4,000 + 700 + 20 + 8
Final answer:

4,728 = 4,000 + 700 + 20 + 8

Applied rules:

• Place Value Multiplication: Each digit multiplied by its place value

• Expanded Form Format: Sum of place values

• Verification: Sum of parts equals original number

2 Expanded form example with zeros
Exercise 2
Write 6,053 in expanded form.
Definition:

Zero in expanded form: Even zeros are included as (0 × place value) = 0

Number
6,053
Expanded Form
6,000 + 0 + 50 + 3
Simplified
6,000 + 50 + 3
Step 1: Identify place values

6 is in thousands place: 6 × 1,000 = 6,000

0 is in hundreds place: 0 × 100 = 0

5 is in tens place: 5 × 10 = 50

3 is in ones place: 3 × 1 = 3

Step 2: Write in expanded form

6,053 = 6,000 + 0 + 50 + 3

Step 3: Simplify by omitting zero terms

6,053 = 6,000 + 50 + 3

Step 4: Verify the calculation

6,000 + 50 + 3 = 6,053 ✓

6,053 = 6,000 + 50 + 3
Final answer:

6,053 = 6,000 + 50 + 3

Applied rules:

• Zero Inclusion: Zeros are written as (0 × place value)

• Simplification: Terms with (0 × place value) can be omitted

• Verification: Sum of parts equals original number

3 Converting expanded form to standard form example
Exercise 3
What number is represented by 8,000 + 300 + 0 + 7?
Definition:

Standard form: The regular way we write numbers without showing place values

Expanded Form
8,000 + 300 + 0 + 7
Standard Form
8,307
Step 1: Add all parts of the expanded form

8,000 + 300 + 0 + 7 = 8,307

Step 2: Verify by converting back to expanded form

8,307 = 8,000 + 300 + 0 + 7 ✓

8,000 + 300 + 0 + 7 = 8,307
Final answer:

The number is 8,307

Applied rules:

• Place Value Addition: Sum all expanded form parts

• Digit Placement: Each part corresponds to a specific place

• Verification: Convert back to ensure accuracy

Expanded Form Examples Rules
\(4,728 = 4,000 + 700 + 20 + 8\)
Expanded Form Example
Ones Place
\(d \times 1\)
Digit × 1
Tens Place
\(d \times 10\)
Digit × 10
Hundreds Place
\(d \times 100\)
Digit × 100
Thousands Place
\(d \times 1,000\)
Digit × 1,000
Key definitions:

Expanded Form: A number expressed as the sum of each digit multiplied by its place value

Place Value: The value of a digit based on its position in a number

Standard Form: The regular way we write numbers (e.g., 4,728)

Digit: Any of the symbols 0-9 used to make numbers

Expanded Form Examples: Specific illustrations of how numbers are broken down into place values

Complete methodology:
  1. Identify positions: Recognize place values (ones, tens, hundreds, thousands, etc.)
  2. Multiplication: Express each digit as (digit × place value)
  3. Addition: Join all parts with plus signs
  4. Verification: Add the expanded parts to confirm they equal the original number
Tip 1: Remember the place value pattern: 1, 10, 100, 1,000...
Tip 2: Zeros in expanded form can be written as (0 × place value) or omitted.
Tip 3: Always verify by adding the expanded parts to get the original number.
Tip 4: Use base-10 blocks to visualize place values for better understanding.
Common errors: Forgetting place values, misplacing digits, confusing expanded form with standard form.
Memory aid: Think of expanded form as "digit times place value".
Formulas to know by heart:

• Expanded Form: Sum of (digit × place value)

• Place value pattern: 1, 10, 100, 1,000, 10,000...

• Verification: Sum of expanded parts = Original number

• Zero rule: (0 × any place value) = 0

Solution: Exercises 4 to 5
4 Multiple expanded form examples
Exercise 4
Write the following numbers in expanded form: 5,604 and 9,080.
Definition:

Multiple examples: Working with several numbers to reinforce the concept

First Number
5,604
Expanded Form
5,000 + 600 + 0 + 4
Second Number
9,080
Expanded Form
9,000 + 0 + 80 + 0
Step 1: Analyze first number (5,604)

5 is in thousands place: 5 × 1,000 = 5,000

6 is in hundreds place: 6 × 100 = 600

0 is in tens place: 0 × 10 = 0

4 is in ones place: 4 × 1 = 4

Step 2: Write first number in expanded form

5,604 = 5,000 + 600 + 0 + 4 = 5,000 + 600 + 4

Step 3: Analyze second number (9,080)

9 is in thousands place: 9 × 1,000 = 9,000

0 is in hundreds place: 0 × 100 = 0

8 is in tens place: 8 × 10 = 80

0 is in ones place: 0 × 1 = 0

Step 4: Write second number in expanded form

9,080 = 9,000 + 0 + 80 + 0 = 9,000 + 80

5,604 = 5,000 + 600 + 4
9,080 = 9,000 + 80
Final answer:

5,604 = 5,000 + 600 + 4

9,080 = 9,000 + 80

Applied rules:

• Multiple examples: Practice with different numbers

• Zero handling: Zeros can be omitted in final form

• Verification: Check that sums equal original numbers

5 Missing digit in expanded form example
Exercise 5
If 7,000 + n + 50 + 3 = 7,453, what is the value of n?
Definition:

Missing digit problem: Finding an unknown value in expanded form

Given
7,000 + n + 50 + 3 = 7,453
Solve for n
n = 7,453 - 7,000 - 50 - 3
Step 1: Set up the equation

7,000 + n + 50 + 3 = 7,453

Step 2: Isolate the unknown

n = 7,453 - 7,000 - 50 - 3

Step 3: Calculate the known values

7,000 + 50 + 3 = 7,053

Step 4: Solve for n

n = 7,453 - 7,053 = 400

Step 5: Verify the answer

7,000 + 400 + 50 + 3 = 7,453 ✓

n = 400
7,000 + 400 + 50 + 3 = 7,453
Final answer:

The value of n is 400

Because 7,000 + 400 + 50 + 3 = 7,453

Applied rules:

• Algebraic reasoning: Treat unknown as variable to solve

• Place value understanding: Each part contributes to total value

• Verification: Substitute back to confirm answer

Complete Summary: Number in Expanded Form Examples
\(d_n \times 10^n + d_{n-1} \times 10^{n-1} + ... + d_1 \times 10^1 + d_0 \times 10^0\)
General Expanded Form Formula
Key definitions:

Expanded Form: A number expressed as the sum of each digit multiplied by its place value

Place Value: The value of a digit based on its position in a number

Standard Form: The usual way we write numbers (e.g., 4,728)

Digit: Any of the symbols 0-9 used to make numbers

Expanded Form Examples: Specific illustrations of how numbers are broken down into place values

Number Sense: Understanding the relationships between numbers and their values

Complete methodology:
  1. Identify positions: Recognize the place value of each digit
  2. Multiplication: Express each digit as (digit × place value)
  3. Addition: Join all parts with plus signs
  4. Verification: Add the expanded parts to confirm they equal the original number
Tip 1: Use the place value pattern: 1, 10, 100, 1,000, 10,000...
Tip 2: Draw a place value chart to organize digits before expanding.
Tip 3: Always verify by calculating the sum of expanded form parts.
Tip 4: Practice reading numbers aloud to reinforce place value understanding.
Common errors: Confusing expanded form with standard form, misplacing digits, forgetting zeros.
Memory aids: Use base-10 blocks, draw charts, remember "digit times place value".
Formulas and Rules to Know:

• Place Value Pattern: ..., 10,000, 1,000, 100, 10, 1

• Expanded Form: Sum of (digit × place value)

• Zero Rule: (0 × any place value) = 0

• Verification: Sum of expanded parts = Original number

• Format: (digit × place value) + (digit × place value) + ...

Expanded Form Examples Visualization: Number Breakdown
Exercise 6: Understanding Expanded Form
Consider the following numbers and their expanded form breakdowns:
4,728 = 4,000 + 700 + 20 + 8
6,053 = 6,000 + 0 + 50 + 3
9,105 = 9,000 + 100 + 0 + 5

Analysis: The chart shows how numbers decompose into expanded form components.

  • 4,728 = 4×1,000 + 7×100 + 2×10 + 8×1 (Four thousand seven hundred twenty-eight)
  • 6,053 = 6×1,000 + 0×100 + 5×10 + 3×1 (Six thousand fifty-three)
  • 9,105 = 9×1,000 + 1×100 + 0×10 + 5×1 (Nine thousand one hundred five)

Questions & Answers

Question: I don't understand why we need to learn expanded form examples. Why can't we just write numbers normally?

Answer: Great question! Expanded form examples are crucial for understanding how our number system works:

  • They help you understand what each digit means in a number
  • They build a foundation for addition and subtraction with regrouping
  • They prepare you for working with larger numbers and decimals later
  • They make it easier to compare numbers and understand their magnitude
  • They show the relationship between digits and their place values

For example, in expanded form (4,000 + 700 + 20 + 8), you can see that the 4 represents 4 thousands (4,000), not just 4. This helps you understand the true value of each digit!

Question: My child gets confused when there are zeros in the expanded form like 6,053 = 6,000 + 0 + 50 + 3. How do I explain this?

Answer: Here's a helpful explanation for zeros in expanded form:

  • In 6,053 = 6,000 + 0 + 50 + 3, the 0 represents 0 hundreds
  • Even though 0 = 0, we include it to show that there's a place for hundreds (even if it's empty)
  • This helps us see that the number is 6,053: 6 thousands, 0 hundreds, 5 tens, 3 ones
  • The zero keeps the 5 in the tens place and the 3 in the ones place in the right positions

You can think of it like having an empty box in a row of boxes. Even though the box is empty, it still takes up space and keeps the other items in their correct positions!

Sometimes we simplify by writing 6,000 + 50 + 3, but including the zero version shows the complete place value structure.

Question: What's the best way to check if my expanded form answer is correct?

Answer: Here are effective verification methods:

  • Add up the expanded parts: If you wrote 4,728 as 4,000 + 700 + 20 + 8, add them: 4,000 + 700 + 20 + 8 = 4,728 ✓
  • Count the digits: Make sure you have one term for each digit in the original number
  • Check place values: Ensure each digit is multiplied by the correct power of 10
  • Use estimation: The largest term should be close to the original number

For example, with 4,728: The largest term (4,000) is close to 4,728, which makes sense. The sum 4,000 + 700 + 20 + 8 = 4,728 confirms the answer is correct!