Expanded Form: Mastering Place Value in 3rd Grade

Learn expanded form: 5 detailed exercises with step-by-step solutions, definitions, and visual learning tools to master place value concepts.

Solution: Exercises 1 to 3
1 Basic expanded form
Exercise 1
Write 247 in expanded form.
Definition:

Expanded form: Writing a number as the sum of the value of each digit based on its place value

Method:
  1. Identify each digit and its place value
  2. Write the value of each digit
  3. Connect with addition signs
Number
247
Expanded
200 + 40 + 7
Step 1: Identify place values

2 is in the hundreds place = 200

4 is in the tens place = 40

7 is in the ones place = 7

Step 2: Write each value

200 + 40 + 7

Step 3: Verify by adding

200 + 40 + 7 = 247 ✓

247 = 200 + 40 + 7
Final answer:

247 = 200 + 40 + 7

Applied rules:

• Place value: Each position has a specific value (ones, tens, hundreds)

• Digit value: Digit × Place value

• Verification: Adding expanded parts gives original number

2 Three-digit expanded form
Exercise 2
Write 583 in expanded form.
Definition:

Three-digit expanded form: Sum of hundreds, tens, and ones values

Number
583
Expanded
500 + 80 + 3
Step 1: Identify each digit's place

5 is in the hundreds place = 500

8 is in the tens place = 80

3 is in the ones place = 3

Step 2: Write expanded form

500 + 80 + 3

Step 3: Check calculation

500 + 80 + 3 = 583 ✓

583 = 500 + 80 + 3
Final answer:

583 = 500 + 80 + 3

Applied rules:

• Place value system: Each position represents 10 times the previous

• Value calculation: Digit × Place value

• Verification: Addition confirms accuracy

3 Four-digit expanded form
Exercise 3
Write 4,267 in expanded form.
Definition:

Four-digit expanded form: Sum of thousands, hundreds, tens, and ones values

Number
4,267
Expanded
4,000 + 200 + 60 + 7
Step 1: Identify all place values

4 is in the thousands place = 4,000

2 is in the hundreds place = 200

6 is in the tens place = 60

7 is in the ones place = 7

Step 2: Write expanded form

4,000 + 200 + 60 + 7

Step 3: Verify result

4,000 + 200 + 60 + 7 = 4,267 ✓

4,267 = 4,000 + 200 + 60 + 7
Final answer:

4,267 = 4,000 + 200 + 60 + 7

Applied rules:

• Thousand place: 4 × 1,000 = 4,000

• Place value sequence: Thousands → Hundreds → Tens → Ones

• Verification: Always check by adding expanded parts

Expanded Form Rules and Methods
ABCD = A×1000 + B×100 + C×10 + D×1
General Expanded Form Formula
Ones Place
D × 1 = D
Rightmost digit value
Tens Place
C × 10 = C0
Second from right
Hundreds Place
B × 100 = B00
Third from right
Key Definitions:

Expanded form: Writing a number as the sum of the value of each digit

Standard form: Writing a number in its normal format (like 247)

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

Step-by-Step Method:
  1. Identify digits: Look at each digit in the number
  2. Find place values: Determine which place each digit occupies
  3. Calculate values: Multiply each digit by its place value
  4. Write expanded form: Connect with addition signs
  5. Verify: Add to confirm you get the original number
Tip 1: Remember the place value sequence: Ones, Tens, Hundreds, Thousands...
Tip 2: Zero digits still count in place value (like 307 = 300 + 0 + 7).
Tip 3: Always verify by adding your expanded form back together.
Common errors: Forgetting zeros, misidentifying place values, incorrect multiplication.
Memory aid: Think of money: $247 is $200 + $40 + $7.
Essential Rules:

• Ones place: Digit × 1

• Tens place: Digit × 10

• Hundreds place: Digit × 100

• Thousands place: Digit × 1,000

• Verification: Always add parts to check

Solution: Exercises 4 to 5
4 Numbers with zeros
Exercise 4
Write 3,040 in expanded form.
Definition:

Numbers with zeros: Zeros hold place value positions but contribute 0 to the sum

Number
3,040
Recognition
3×1000 + 0×100 + 4×10 + 0×1
Expanded
3,000 + 0 + 40 + 0
Step 1: Identify each digit and place

3 is in the thousands place = 3,000

0 is in the hundreds place = 0

4 is in the tens place = 40

0 is in the ones place = 0

Step 2: Write expanded form

3,000 + 0 + 40 + 0

Step 3: Verify result

3,000 + 0 + 40 + 0 = 3,040 ✓

3,040 = 3,000 + 0 + 40 + 0
Final answer:

3,040 = 3,000 + 0 + 40 + 0

Applied rules:

• Zero handling: Zeros still occupy place values

• Place preservation: Don't skip zero positions

• Verification: Always confirm by adding

5 Mixed place values
Exercise 5
Write 7,509 in expanded form.
Definition:

Mixed place values: Numbers containing various combinations of non-zero and zero digits

Number
7,509
Place values
7×1000 + 5×100 + 0×10 + 9×1
Expanded
7,000 + 500 + 0 + 9
Step 1: Identify all digits and places

7 is in the thousands place = 7,000

5 is in the hundreds place = 500

0 is in the tens place = 0

9 is in the ones place = 9

Step 2: Write expanded form

7,000 + 500 + 0 + 9

Step 3: Verify the result

7,000 + 500 + 0 + 9 = 7,509 ✓

7,509 = 7,000 + 500 + 0 + 9
Final answer:

7,509 = 7,000 + 500 + 0 + 9

Applied rules:

• Systematic approach: Go from left to right through each place

• Zero inclusion: Include zeros in expanded form

• Verification: Always check by addition

Expanded Form Laws, Methods, and Definitions
ABCD = A×1000 + B×100 + C×10 + D×1
Expanded Form Formula
Key definitions:

Expanded form: Writing a number as the sum of the value of each digit

Standard form: Writing a number in its normal format (like 247)

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

Base ten system: Our number system where each place is worth 10 times the previous

Complete methodology:
  1. Identify the number: Look at each digit and its position
  2. Determine place values: Thousands, hundreds, tens, ones
  3. Calculate each value: Multiply digit by its place value
  4. Write expanded form: Add all values with + signs
  5. Verify result: Add to ensure you get original number
Tip 1: Use the acronym HTU: Hundreds, Tens, Units (or Ones).
Tip 2: Count from right to left: 1st digit is ones, 2nd is tens, 3rd is hundreds.
Tip 3: Use money as a model: $347 = $300 + $40 + $7.
Tip 4: Always include zeros in expanded form to maintain place value.
Common errors: Forgetting zeros, misplacing commas, mixing up place values.
Exam preparation: Practice with various digit lengths, including numbers with zeros.
Place Value Rules:

• Ones place: Rightmost digit, value = digit × 1

• Tens place: Second from right, value = digit × 10

• Hundreds place: Third from right, value = digit × 100

• Thousands place: Fourth from right, value = digit × 1,000

• Verification: Adding expanded parts gives original number

Visual Place Value Exercise: Understanding Number Structure
Exercise 6: Place Value Blocks
Consider the number 4,267 and visualize it using place value blocks:
• 4 thousand blocks (4,000)
• 2 hundred blocks (200)
• 6 ten blocks (60)
• 7 one blocks (7)
4,000
Thousands
200
Hundreds
60
Tens
7
Ones
Total: 4,000 + 200 + 60 + 7 = 4,267

Analysis: Place value blocks help visualize the expanded form concept:

  • Each digit contributes a specific amount based on its position
  • The total value is the sum of all position contributions
  • This visualization helps understand why expanded form works

Questions & Answers

Question: I don't understand why we write numbers in expanded form. What's the point of it?

Answer: Great question! Expanded form helps us understand how our number system works. It breaks down numbers so we can see the value of each digit:

  • It shows that in 247, the "2" actually represents 200, not just 2
  • It helps with addition and subtraction by showing place values
  • It builds the foundation for understanding larger numbers
  • It connects to real-world concepts like money ($247 = $200 + $40 + $7)

Think of it like taking apart a toy to see how it's built - expanded form shows us how numbers are constructed from their place values.

Question: When I have a number like 307, do I still write the zero part in expanded form?

Answer: Yes, you should include the zero in expanded form! For 307:

  • 3 is in the hundreds place = 300
  • 0 is in the tens place = 0
  • 7 is in the ones place = 7

So 307 = 300 + 0 + 7. The zero is important because it holds the tens place, even though it contributes nothing to the total value. Without the zero, we might forget that the 3 represents 300, not 30.

This is especially important when comparing numbers or doing calculations.

Question: My child is struggling with expanded form. Are there any tricks to help remember place values?

Answer: Absolutely! Here are some helpful strategies:

  • Count from the right: Start with "ones," then "tens," then "hundreds," then "thousands"
  • Money connection: Link to dollars: $247 = $200 bills + $40 + $7
  • Visual aids: Use place value charts or blocks to physically represent each digit
  • Rhyme: "From right to left, ones, tens, hundreds, thousands - that's the place value way!"

Practice with real-world examples like prices, ages, or house numbers to make it more meaningful. Consistent daily practice with small numbers first will build confidence.