Expanded Notation Worksheets Grade 3: Mastering Place Value in 3rd Grade

Complete expanded notation exercises for Grade 3: practice converting between standard form and expanded form, understand place value concepts, and develop number sense skills.

Expanded Notation Worksheets Grade 3: Problems 1 to 3
1 Basic Tens and Ones
Worksheet 1
Write 58 in expanded notation.
Definition:

Expanded notation for Grade 3: Writing a number as the sum of each digit multiplied by its place value (tens, ones).

Method for expanded notation:
  1. Identify the place value of each digit (tens, ones)
  2. Multiply each digit by its place value
  3. Write the sum of these products
Tens
5
× 10 = 50
Ones
8
× 1 = 8
5
8
58 = 50 + 8
Additional Practice Problems:

• Write 34 in expanded notation

• Write 79 in expanded notation

• Write 26 in expanded notation

Step 1: Identify place values

In 58: 5 is in tens place, 8 is in ones place

Step 2: Multiply each digit by its place value

5 × 10 = 50; 8 × 1 = 8

Step 3: Write the sum

Combine all values: 50 + 8

58 = 50 + 8
Final answer:

58 = 50 + 8

Applied rules:

• Place value system: Each position represents a power of 10

• Expanded form: Express number as sum of place values

• Value calculation: Digit × Place value = Component value

2 With Zero
Worksheet 2
Write 40 in expanded notation.
Definition:

Expanded notation with zero: When a number has zero in the ones place, we still include it in expanded form.

Tens
4
× 10 = 40
Ones
0
× 1 = 0
4
0
40 = 40 + 0
Additional Practice Problems:

• Write 30 in expanded notation

• Write 70 in expanded notation

• Write 90 in expanded notation

Step 1: Identify place values

In 40: 4 is in tens place, 0 is in ones place

Step 2: Handle the zero

Even though 0 × 1 = 0, we include it in the expanded form to maintain place value structure

Step 3: Calculate and write

4 × 10 = 40; 0 × 1 = 0

40 = 40 + 0
Final answer:

40 = 40 + 0

Applied rules:

• Zero inclusion: Include zeros in expanded notation to maintain place value structure

• Place holding: Zeros hold positions even when they contribute zero value

• Completeness: Every digit position should be represented

3 Three-Digit Numbers
Worksheet 3
Write 347 in expanded notation.
Definition:

Three-digit expanded notation: Writing a three-digit number as the sum of hundreds, tens, and ones.

Hundreds
3
× 100 = 300
Tens
4
× 10 = 40
Ones
7
× 1 = 7
3
4
7
347 = 300 + 40 + 7
Additional Practice Problems:

• Write 528 in expanded notation

• Write 691 in expanded notation

• Write 405 in expanded notation

Step 1: Identify place values

In 347: 3 is in hundreds place, 4 in tens, 7 in ones

Step 2: Multiply each digit by its place value

3 × 100 = 300; 4 × 10 = 40; 7 × 1 = 7

Step 3: Write the sum

Combine all values: 300 + 40 + 7

347 = 300 + 40 + 7
Final answer:

347 = 300 + 40 + 7

Applied rules:

• Three-digit numbers: Include hundreds, tens, and ones

• Place value system: Each position represents a power of 10

• Expanded form: Express number as sum of place values

Expanded Notation Rules and Methods for Grade 3
234 = 200 + 30 + 4
Standard to Expanded Form
Ones Place
Digit × 1
Units
Tens Place
Digit × 10
Groups of Ten
Hundreds Place
Digit × 100
Groups of Hundred
Key definitions:

Place Value: The value of a digit based on its position in a number (ones, tens, hundreds).

Expanded Form: Writing a number as the sum of each digit's value.

Standard Form: The normal way we write numbers using digits.

Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers.

Complete methodology:
  1. Identify digits: Look at each digit in the number
  2. Determine place values: Identify the value of each position (ones, tens, hundreds)
  3. Multiply: Multiply each digit by its place value
  4. Add: Sum all the products to get expanded form
  5. Verify: Check that your expanded form adds up to the original number
Tip 1: Start from the left (highest place value) and work to the right.
Tip 2: Remember that each place value is 10 times the one to its right.
Tip 3: Don't skip zeros - they hold important place value positions.
Tip 4: Practice with smaller numbers first, then move to larger ones.
Common errors: Forgetting to multiply by place value, skipping zeros, miscounting place values.
Memorization trick: "Multiply each digit by its position value and add them together."
Expanded Notation Worksheets Grade 3: Problems 4 to 5
4 Numbers with Zeros
Worksheet 4
Write 508 in expanded notation.
Definition:

Numbers with zeros in expanded notation: When a number has zero in any place value, we still include that place in expanded form.

Hundreds
5
× 100 = 500
Tens
0
× 10 = 0
Ones
8
× 1 = 8
5
0
8
508 = 500 + 0 + 8
Additional Practice Problems:

• Write 307 in expanded notation

• Write 802 in expanded notation

• Write 400 in expanded notation

Step 1: Identify place values

In 508: 5 is in hundreds place, 0 in tens, 8 in ones

Step 2: Handle the zero

Even though 0 × 10 = 0, we include it in the expanded form to maintain place value structure

Step 3: Calculate and write

5 × 100 = 500; 0 × 10 = 0; 8 × 1 = 8

508 = 500 + 0 + 8
Final answer:

508 = 500 + 0 + 8

Applied rules:

• Zero inclusion: Include zeros in expanded notation to maintain place value structure

• Place holding: Zeros hold positions even when they contribute zero value

• Completeness: Every digit position should be represented

5 Mixed Practice
Worksheet 5
Complete the following conversions: 642, 309, and 750.
Definition:

Mixed practice: Working with various numbers helps solidify understanding of place value concepts.

Problem Set Solutions:
Problem 1: 642

642 = 600 + 40 + 2

Problem 2: 309

309 = 300 + 0 + 9

Problem 3: 750

750 = 700 + 50 + 0

Step 1: Process each number individually

Follow the same method for each number: identify place values, multiply by place value, sum components

Step 2: Verify each conversion

Check that the expanded form adds up to the original number

Step 3: Notice patterns

Numbers with trailing zeros still include those zeros in expanded form

642 = 600 + 40 + 2
309 = 300 + 0 + 9
750 = 700 + 50 + 0
Final answers:

642 = 600 + 40 + 2

309 = 300 + 0 + 9

750 = 700 + 50 + 0

Applied rules:

• Consistent method: Same process applies to all numbers

• Zero inclusion: Include zeros in expanded form to maintain place value structure

• Verification: The sum of components should equal the original number

Expanded Notation Worksheets Grade 3 Summary
456 = 400 + 50 + 6
Expanded Notation Formula
Key definitions:

Place Value: The value of a digit based on its position in a number (ones, tens, hundreds).

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

Standard Form: The usual way we write numbers using digits without showing place value breakdown.

Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers.

Place Value Chart: A visual representation showing the value of each position in a number.

Complete methodology:
  1. Read the number: Identify each digit and its position
  2. Assign place values: Determine the value each digit position represents
  3. Multiply digits by place values: Calculate each digit's contribution
  4. Write as addition: Combine all components with plus signs
  5. Verify: Check that the sum equals the original number
Tip 1: Use a place value chart to organize your work systematically.
Tip 2: Remember: each place value is 10 times the one to its right.
Tip 3: Practice reading numbers aloud to reinforce place value understanding.
Tip 4: Check your work by adding the expanded components to see if you get the original number.
Common mistakes: Forgetting to include zeros in expanded form, miscounting place values, confusing digits with place values.
Memory aid: "Each digit tells you how many of that place value there are."
Place Value System for Grade 3:

• Ones place: 1 = 1

• Tens place: 1 = 10

• Hundreds place: 1 = 100

• Pattern: Each place value is 10 times the previous one

Simple Example
45 = 40 + 5
Standard, Expanded
Medium Example
327 = 300 + 20 + 7
Standard, Expanded
Complex Example
5,048 = 5,000 + 0 + 40 + 8
Standard, Expanded
Large Example
12,563 = 10,000 + 2,000 + 500 + 60 + 3
Standard, Expanded

Questions & Answers

Question: Why do we need to learn expanded notation? It seems harder than just writing the number.

Answer: Great question! Expanded notation helps you understand what numbers really mean:

  • Understand numbers: It shows you that 234 is made of 200 + 30 + 4
  • Easier math: It makes addition and subtraction easier later
  • Big numbers: It prepares you for bigger numbers in higher grades
  • Real life: It helps count things like money and groups of items

Expanded notation builds the foundation for understanding how our number system works!

Question: My child gets confused with the expanded form of numbers like 405. How can I help them understand?

Answer: Here are effective strategies to help with numbers containing zeros:

  • Visual aids: Use place value charts to clearly show where each digit goes
  • Verbal explanation: Say "There are 0 tens" rather than skipping the place
  • Physical objects: Use base-10 blocks to show empty places
  • Pattern recognition: Emphasize that every position must be accounted for

Example: In 405, emphasize "4 hundreds, 0 tens, 5 ones" even though there are 0 tens. The zero still holds the place and appears in expanded form as 0.

Practice with numbers like 102, 304, and 500 to build confidence with zeros.

Question: Are there more place values beyond hundreds? What comes next?

Answer: Yes! The place value system continues:

  • Thousands: Fourth digit from right (1,000)
  • Ten thousands: Fifth digit from right (10,000)
  • Hundred thousands: Sixth digit from right (100,000)
  • Pattern continues: Each place is 10 times the previous one

Example: In 1,234:

1 is in thousands place (1,000), 2 in hundreds (200), 3 in tens (30), 4 in ones (4)

For now, focus on hundreds, but know that the same pattern applies to larger numbers!