Expanded Form Worksheets for Grade 3: Mastering Place Value

Learn expanded form: breaking down numbers into their place value components. Includes 5 detailed exercises with step-by-step solutions, definitions, rules, and methods for grade 3 students.

Solution: Exercises 1 to 3
1 Three-Digit Number
Exercise 1
Write 347 in expanded form.
Definition:

Expanded form: Writing a number as the sum of each digit multiplied by its place value.

Method for expanded form:
  1. Look at each digit in the number
  2. Determine the place value of each digit (ones, tens, hundreds)
  3. Multiply each digit by its place value
  4. Add all the products together
Number
347
Place Values
300 + 40 + 7
Step 1: Identify digits and positions

347 has digits: 3 (hundreds place), 4 (tens place), 7 (ones place)

Step 2: Determine place values

3 × 100 = 300, 4 × 10 = 40, 7 × 1 = 7

Step 3: Write in expanded form

347 = 300 + 40 + 7

3
Hundreds
3 × 100 = 300
4
Tens
4 × 10 = 40
7
Ones
7 × 1 = 7
347 = 300 + 40 + 7
Final answer:

347 in expanded form is 300 + 40 + 7

Applied rules:

• Place value rule: Each digit's value depends on its position

• Expanded form rule: Sum of each digit × its place value

• Position system: Rightmost digit is ones, then tens, then hundreds...

2 Four-Digit Number
Exercise 2
Write 1,256 in expanded form.
Definition:

Four-digit number expanded form: Th × 1000 + H × 100 + T × 10 + O × 1

Number
1,256
Expanded
1000 + 200 + 50 + 6
Step 1: Identify digits and positions

1,256 has: 1 in thousands place, 2 in hundreds place, 5 in tens place, 6 in ones place

Step 2: Calculate place values

1 × 1000 = 1000, 2 × 100 = 200, 5 × 10 = 50, 6 × 1 = 6

Step 3: Write expanded form

1,256 = 1000 + 200 + 50 + 6

1
Thousands
1 × 1000 = 1000
2
Hundreds
2 × 100 = 200
5
Tens
5 × 10 = 50
6
Ones
6 × 1 = 6
1,256 = 1000 + 200 + 50 + 6
Final answer:

1,256 in expanded form is 1000 + 200 + 50 + 6

Applied rules:

• Thousands rule: 4th digit from right represents thousands

• Position progression: Each position to the left is 10 times greater

• Place value system: Thousands, hundreds, tens, ones from left to right

3 Number with Middle Zeros
Exercise 3
Write 4,050 in expanded form.
Definition:

Numbers with middle zeros: Include zero place values in expanded form.

Number
4,050
Expanded
4000 + 0 + 50 + 0
Simplified
4000 + 50
Step 1: Identify digits and positions

4,050 has: 4 in thousands place, 0 in hundreds place, 5 in tens place, 0 in ones place

Step 2: Calculate place values

4 × 1000 = 4000, 0 × 100 = 0, 5 × 10 = 50, 0 × 1 = 0

Step 3: Write expanded form

4,050 = 4000 + 0 + 50 + 0, which simplifies to 4000 + 50

4
Thousands
4 × 1000 = 4000
0
Hundreds
0 × 100 = 0
5
Tens
5 × 10 = 50
0
Ones
0 × 1 = 0
4,050 = 4000 + 0 + 50 + 0 = 4000 + 50
Final answer:

4,050 in expanded form is 4000 + 0 + 50 + 0 (or 4000 + 50)

Applied rules:

• Zero rule: Include zero place values in expanded form

• Simplification: Addends with zero can be omitted in final answer

• Position rule: Zero still holds its place value position

Rules and methods, laws,...
3,456 = 3000 + 400 + 50 + 6
Basic Expanded Form
Ones Place
Digit × 1
Rightmost digit
Tens Place
Digit × 10
Second from right
Hundreds Place
Digit × 100
Third from right
Thousands Place
Digit × 1000
Fourth from right
Key definitions:

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

Standard form: Regular way of writing numbers (e.g., 3,456)

Expanded form: Breaking a number into the sum of its place values

Complete methodology:
  1. Count digits: Determine the number of digits in the number
  2. Identify positions: Recognize which digit is in each place value
  3. Calculate values: Multiply each digit by its corresponding place value
  4. Combine: Add all the products together
  5. Verify: Check that the sum equals the original number
Tip 1: Start from the rightmost digit (ones place) and move left.
Tip 2: Each position to the left is 10 times greater than the previous.
Tip 3: Practice with smaller numbers first, then progress to larger ones.
Tip 4: Always verify your answer by adding the expanded parts.
Common errors: Misidentifying place values, forgetting zeros, miscalculating products.
Memorization aid: Think of place values as: Ones, Tens, Hundreds, Thousands (OTHT).
Formulas to know by heart:

• Ones place: Digit × 1

• Tens place: Digit × 10

• Hundreds place: Digit × 100

• Thousands place: Digit × 1000

• Expanded form: Sum of (Digit × Place Value)

Solution: Exercises 4 to 5
4 Large Four-Digit Number
Exercise 4
Write 7,832 in expanded form.
Definition:

Four-digit number expanded form: Th × 1000 + H × 100 + T × 10 + O × 1

Number
7,832
Expanded
7000 + 800 + 30 + 2
Step 1: Identify digits and positions

7,832 has: 7 in thousands place, 8 in hundreds place, 3 in tens place, 2 in ones place

Step 2: Calculate place values

7 × 1000 = 7000, 8 × 100 = 800, 3 × 10 = 30, 2 × 1 = 2

Step 3: Write expanded form

7,832 = 7000 + 800 + 30 + 2

7
Thousands
7 × 1000 = 7000
8
Hundreds
8 × 100 = 800
3
Tens
3 × 10 = 30
2
Ones
2 × 1 = 2
7,832 = 7000 + 800 + 30 + 2
Final answer:

7,832 in expanded form is 7000 + 800 + 30 + 2

Applied rules:

• Position rule: Thousands, hundreds, tens, ones from left to right

• Place value rule: Each position is 10 times greater than the next

• Verification rule: Add expanded parts to check accuracy

5 Mixed Practice
Exercise 5
Write 5,009 in expanded form.
Definition:

Numbers with multiple zeros: Include zero place values in expanded form.

Number
5,009
Expanded
5000 + 0 + 0 + 9
Simplified
5000 + 9
Step 1: Identify digits and positions

5,009 has: 5 in thousands place, 0 in hundreds place, 0 in tens place, 9 in ones place

Step 2: Calculate place values

5 × 1000 = 5000, 0 × 100 = 0, 0 × 10 = 0, 9 × 1 = 9

Step 3: Write expanded form

5,009 = 5000 + 0 + 0 + 9, which simplifies to 5000 + 9

5
Thousands
5 × 1000 = 5000
0
Hundreds
0 × 100 = 0
0
Tens
0 × 10 = 0
9
Ones
9 × 1 = 9
5,009 = 5000 + 0 + 0 + 9 = 5000 + 9
Final answer:

5,009 in expanded form is 5000 + 0 + 0 + 9 (or 5000 + 9)

Applied rules:

• Zero rule: Include all zero place values in expanded form

• Simplification: Addends with zero can be omitted in final answer

• Position rule: Each zero still holds its place value position

Place Value and Expanded Form Rules, Methods, and Definitions
4,567 = 4000 + 500 + 60 + 7
Expanded Form Pattern
Key definitions:

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

Standard form: Regular way of writing numbers (e.g., 4,567)

Expanded form: Breaking a number into the sum of its place values

Ones: Single units (rightmost digit)

Tens: Groups of ten (second digit from right)

Hundreds: Groups of one hundred (third digit from right)

Thousands: Groups of one thousand (fourth digit from right)

Complete methodology:
  1. Analyze the number: Count digits and identify positions
  2. Assign place values: Match each digit to its place value
  3. Calculate products: Multiply each digit by its place value
  4. Write sum: Express as addition of all place values
  5. Verify result: Add components to check if they equal original number
Tip 1: Remember the place value pattern: Ones, Tens, Hundreds, Thousands...
Tip 2: Each place value is 10 times larger than the one to its right.
Tip 3: When converting back to standard form, add all expanded parts.
Tip 4: Use base-10 blocks or charts to visualize place values.
Common errors: Mixing up place values, forgetting to include zeros, miscounting positions.
Practice tip: Use expanded form to understand number relationships and comparisons.
Formulas to know by heart:

• Ones place: Digit × 1

• Tens place: Digit × 10

• Hundreds place: Digit × 100

• Thousands place: Digit × 1000

• Expanded form: Sum of (Digit × Place Value)

Questions & Answers

Question: My grade 3 students are struggling with four-digit numbers in expanded form. How can I help them understand thousands place?

Answer: Great question! For grade 3 students, focus on concrete representations:

  • Use base-10 blocks: Show 1000 blocks as a cube, 100 blocks as a flat square, 10 blocks as a rod, 1 block as a cube
  • Grouping activity: Have students count 10 groups of 100 to make 1000
  • Visual representation: Draw 1000 boxes for thousands, 100 boxes for hundreds, 10 boxes for tens, 1 box for ones
  • Real-world connection: Compare to 1000 meters in a kilometer or 1000 grams in a kilogram

Example: For 4,567, show 4 large cubes (4000), 5 flat squares (500), 6 rods (60), and 7 small cubes (7). This makes the "4000 + 500 + 60 + 7" concept tangible!

Question: My child gets confused when there are multiple zeros in a number like 5,009. Should they write "5000 + 0 + 0 + 9" or "5000 + 9"?

Answer: Both forms are mathematically correct, but for learning purposes:

  • Complete form: 5,009 = 5000 + 0 + 0 + 9 (shows all place values including zeros)
  • Simplified form: 5,009 = 5000 + 9 (omits zero addends for efficiency)

For grade 3 students, I recommend starting with the complete form to emphasize that each place exists even if it's zero. As they become more confident, "5000 + 9" is acceptable since adding zero doesn't change the sum.

The key is understanding that zeros in the hundreds and tens places represent no hundreds and no tens, not that those places don't exist.

Question: Why do we need to learn expanded form? When will I ever use this in real life?

Answer: Expanded form helps you understand numbers much better! Here are some ways you'll use it:

  • Counting money: Understanding that $4,567 is $4000 + $500 + $60 + $7
  • Shopping: Comparing prices like $1,200 vs $2,000
  • Playing games: Understanding scores and points
  • Measuring: Understanding that 5,009 meters is 5000 + 9 meters
  • Future math: Essential foundation for bigger numbers and harder math

Think of expanded form as learning the "ingredients" that make up numbers - just like knowing what's in your favorite meal helps you understand it better!

Detailed Summary: Place Value and Expanded Form for Grade 3

Key Concepts & Definitions

Place Value: The value of a digit based on its position in a number. Each position has a different value.

Standard Form: The regular way we write numbers (like 1,234, 4,567, 5,009).

Expanded Form: Writing a number as the sum of each digit multiplied by its place value.

Ones Place: The rightmost digit represents single units.

Tens Place: The second digit from the right represents groups of ten.

Hundreds Place: The third digit from the right represents groups of one hundred.

Thousands Place: The fourth digit from the right represents groups of one thousand.

Core Rules & Laws

Place Value Rule: Each digit's value depends on its position in the number.

Position Rule: From right to left: ones, tens, hundreds, thousands, ten-thousands...

Multiplication Rule: Multiply each digit by its place value (1 for ones, 10 for tens, 100 for hundreds, 1000 for thousands).

Addition Rule: Sum all the place values to get the expanded form.

Verification Rule: Adding the expanded parts should equal the original number.

Zero Rule: Include zero place values in expanded form even if they can be simplified.

Step-by-Step Methods
  1. Count digits: Look at how many digits are in the number
  2. Identify positions: Figure out which digit is in thousands, hundreds, tens, and ones places
  3. Calculate place values: Multiply each digit by its place value (thousands × 1000, hundreds × 100, tens × 10, ones × 1)
  4. Write expanded form: Add the calculated values together
  5. Verify answer: Add the expanded parts to make sure they equal the original number
Examples (Simple to Advanced)
Three-digit: 347 = 300 + 40 + 7
Four-digit: 1,256 = 1000 + 200 + 50 + 6
Middle zeros: 4,050 = 4000 + 0 + 50 + 0
Large number: 7,832 = 7000 + 800 + 30 + 2
Multiple zeros: 5,009 = 5000 + 0 + 0 + 9
Memory Tip: Remember OTHT: Ones, Tens, Hundreds, Thousands - from right to left!
Position Trick: Count from the right: 1st is ones, 2nd is tens, 3rd is hundreds, 4th is thousands.
Verification: Always add your expanded parts to check if they equal the original number.
Zero Reminder: Even if a place has zero, it still counts in expanded form (like 4,050 = 4000 + 0 + 50 + 0).
Real Life: Expanded form helps with counting money, measuring distances, and comparing large numbers.
Common Pitfalls & Tips

Common Mistakes: Mixing up place values, forgetting to multiply by place value, skipping zeros, miscounting positions.

Helpful Tips: Use visual aids like base-10 blocks, count by tens/hundreds/thousands aloud, practice with real objects, always check your work.

Success Strategy: Start with three-digit numbers, gradually increase to four-digit numbers, use manipulatives for hands-on learning.