Solved Exercises on Expanded Form of Whole Numbers in Grade 4

Master expanded form of whole numbers: place value decomposition, digit representation, and number composition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic place value decomposition
Exercise 1
Write the expanded form of: 3,456
Definition:

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

Place Value Method:
  1. Identify the place value of each digit (thousands, hundreds, tens, ones)
  2. Multiply each digit by its place value
  3. Add all the products together
Number
3,456
Expanded
3,000 + 400 + 50 + 6
Step 1: Identify place values

3 is in thousands place (3 × 1,000 = 3,000)

4 is in hundreds place (4 × 100 = 400)

5 is in tens place (5 × 10 = 50)

6 is in ones place (6 × 1 = 6)

Step 2: Write as addition of place values

3,456 = 3,000 + 400 + 50 + 6

Step 3: Verify the expansion

3,000 + 400 + 50 + 6 = 3,456 ✓

3,456 = 3,000 + 400 + 50 + 6
Final answer:

3,456 = 3,000 + 400 + 50 + 6

Applied rules:

• Place Value: Each digit has a specific value based on position

• Position System: Right to left: ones, tens, hundreds, thousands

• Decomposition: Break down into parts that sum to original number

2 Expanded form with zeros
Exercise 2
Write the expanded form of: 5,073
Definition:

Zero in expanded form: Even zeros represent their place value (e.g., 0 hundreds = 0)

Number
5,073
Expanded
5,000 + 0 + 70 + 3
Simplified
5,000 + 70 + 3
Step 1: Identify place values

5 is in thousands place (5 × 1,000 = 5,000)

0 is in hundreds place (0 × 100 = 0)

7 is in tens place (7 × 10 = 70)

3 is in ones place (3 × 1 = 3)

Step 2: Write as addition of place values

5,073 = 5,000 + 0 + 70 + 3

Step 3: Simplify by removing zero term

5,073 = 5,000 + 70 + 3

5,073 = 5,000 + 70 + 3
Final answer:

5,073 = 5,000 + 70 + 3

Applied rules:

• Zero Place Value: Zeros still represent their position's value

• Simplification: Adding zero doesn't change the sum

• Place Recognition: Identify all positions even with zeros

3 Converting expanded to standard form
Exercise 3
Write in standard form: 7,000 + 400 + 0 + 8
Definition:

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

Expanded
7,000 + 400 + 0 + 8
Standard
7,408
Step 1: Identify each place value

7,000 → 7 in thousands place

400 → 4 in hundreds place

0 → 0 in tens place

8 → 8 in ones place

Step 2: Combine the digits in order

Thousands: 7, Hundreds: 4, Tens: 0, Ones: 8

So we get 7,408

Step 3: Verify by converting back to expanded form

7,408 = 7,000 + 400 + 0 + 8 ✓

Step 4: Final answer

7,000 + 400 + 0 + 8 = 7,408

7,000 + 400 + 0 + 8 = 7,408
Final answer:

7,000 + 400 + 0 + 8 = 7,408

Applied rules:

• Place Value Addition: Sum all expanded parts to get standard form

• Digit Placement: Each part corresponds to a specific place

• Verification: Convert back to ensure accuracy

Place Value System and Expanded Form Rules (Whole Numbers)
\(3,456 = 3,000 + 400 + 50 + 6\)
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:

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

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

Standard Form: The regular way we write numbers

Whole Numbers: Counting numbers including zero (0, 1, 2, 3, ...)

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

Value: The worth of a digit based on its position

Complete methodology:
  1. Identify positions: Recognize thousands, hundreds, tens, ones
  2. Determine values: Multiply each digit by its place value
  3. Express as sum: Write the addition of all place values
  4. Verify: Check that the sum equals the original number
Tip 1: Remember the order: Thousands, Hundreds, Tens, Ones (THOUS).
Tip 2: Zeros in expanded form can be omitted in the final answer.
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, ignoring zeros.
Memory aid: Use "THOUS" (Thousands, Hundreds, Tens, Ones) to remember the order.
Formulas to know by heart:

• Place value: Digit × Position value (1, 10, 100, 1000...)

• Expanded form: Sum of all place values

• Standard form: Regular number notation

• Verification: Sum of expanded parts = Original number

Solution: Exercises 4 to 5
4 Word problem application
Exercise 4
A school has 8,240 students. Write this number in expanded form and explain what each part represents.
Definition:

Word problem conversion: Translate real-world quantities into mathematical forms

Number
8,240
Expanded
8,000 + 200 + 40 + 0
Simplified
8,000 + 200 + 40
Step 1: Identify each digit's place value

8 is in thousands place (8 × 1,000 = 8,000)

2 is in hundreds place (2 × 100 = 200)

4 is in tens place (4 × 10 = 40)

0 is in ones place (0 × 1 = 0)

Step 2: Write in expanded form

8,240 = 8,000 + 200 + 40 + 0

Step 3: Simplify by removing zero term

8,240 = 8,000 + 200 + 40

Step 4: Interpret the meaning

8,000: Eight thousand students

200: Two hundred students

40: Forty students

Total: 8,240 students

8,240 = 8,000 + 200 + 40
Final answer:

8,240 = 8,000 + 200 + 40

This means the school has 8 thousand students, 2 hundred students, and 4 tens of students.

Applied rules:

• Real-world application: Connect math to practical situations

• Place value understanding: Each digit represents a specific quantity

• Context interpretation: Explain what each part means

5 Multiple representations
Exercise 5
Show the number 6,709 in three different ways: standard form, expanded form, and word form.
Definition:

Multiple representations: Same number shown in different mathematical forms

Standard
6,709
Expanded
6,000 + 700 + 0 + 9
Word
Six thousand seven hundred nine
Step 1: Standard form

6,709 (regular number notation)

Step 2: Expanded form

6,709 = 6,000 + 700 + 0 + 9

(6×1,000) + (7×100) + (0×10) + (9×1)

Step 3: Word form

Read the number aloud: Six thousand seven hundred nine

Step 4: Verify all forms are equivalent

6,000 + 700 + 0 + 9 = 6,709 ✓

Standard: 6,709
Expanded: 6,000 + 700 + 9
Word: Six thousand seven hundred nine
Final answer:

Standard form: 6,709

Expanded form: 6,000 + 700 + 9

Word form: Six thousand seven hundred nine

Applied rules:

• Number equivalence: All forms represent the same quantity

• Conversion skills: Practice moving between different representations

• Verification: Confirm all forms equal the same value

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

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

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

Standard Form: The usual way we write numbers (e.g., 3,456)

Word Form: Numbers written out in words (e.g., three thousand four hundred fifty-six)

Whole Numbers: The set of non-negative integers (0, 1, 2, 3, 4, 5, ...)

Digit: Any of the ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) used to make numbers

Complete methodology:
  1. Position identification: Identify the place value of each digit (right to left)
  2. Multiplication: Multiply each digit by its corresponding power of 10
  3. Addition: Express the number as the sum of all place values
  4. Verification: Add the expanded parts to confirm they equal the original number
Tip 1: Use the acronym THOUS (Thousands, Hundreds, Tens, Ones) to remember place value order.
Tip 2: Draw a place value chart to organize digits before expanding.
Tip 3: Always include zeros in your place value analysis, even if they simplify out.
Tip 4: Practice reading numbers aloud to reinforce place value understanding.
Common errors: Misplacing digits, forgetting zeros, confusing place values, adding instead of multiplying.
Memory aids: Use base-10 blocks, draw charts, count positions from right to left starting at 0.
Formulas and Rules to Know:

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

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

• Zero Rule: Zeros contribute 0 to the sum but indicate position

• Verification: Expanded parts must sum to original number

• Whole Numbers: Start from 0 and increase by 1 (0, 1, 2, 3, ...)

Place Value Visualization: Whole Number Decomposition
Exercise 6: Understanding Place Values
Consider the following numbers and their place value breakdowns:
4,567 = 4,000 + 500 + 60 + 7
8,032 = 8,000 + 0 + 30 + 2
9,105 = 9,000 + 100 + 0 + 5

Analysis: The chart shows how numbers decompose into their place value components.

  • 4,567 = 4×1,000 + 5×100 + 6×10 + 7×1 (Standard to Expanded)
  • 8,032 = 8×1,000 + 0×100 + 3×10 + 2×1 (With Zero in Hundreds)
  • 9,105 = 9×1,000 + 1×100 + 0×10 + 5×1 (With Zero in Tens)

Questions & Answers

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

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

  • It helps you understand place value - knowing that in 3,456, the 3 represents 3,000, not just 3
  • It builds a foundation for addition and subtraction with regrouping
  • It prepares you for working with larger numbers and decimals later
  • It makes it easier to compare numbers and understand their magnitude

Think of it like understanding how money works: $3,456.78 means 3 thousands ($3,000), 4 hundreds ($400), 5 tens ($50), 6 ones ($6), etc. Expanded form does the same thing for whole numbers!

Question: My child gets confused when there are zeros in the middle of a number like 5,073. How do I explain the expanded form?

Answer: Here's a helpful approach for numbers with zeros:

  • Use a place value chart to show every position: Thousands | Hundreds | Tens | Ones
  • Write 5,073 in the chart: 5 in thousands, 0 in hundreds, 7 in tens, 3 in ones
  • Even though the hundreds digit is 0, it still represents 0 hundreds = 0
  • So: 5,073 = 5,000 + 0 + 70 + 3, which simplifies to 5,000 + 70 + 3

You can also use manipulatives like base-10 blocks or draw the concept: 5 thousand blocks, 0 hundred blocks, 7 ten sticks, 3 unit cubes. The absence of hundred blocks still represents 0 hundreds!

The zero keeps the other digits in their correct places!

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

Answer: Here are effective verification methods:

  • Add up the expanded parts: If you wrote 3,456 as 3,000 + 400 + 50 + 6, add them: 3,000 + 400 + 50 + 6 = 3,456 ✓
  • 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 3,456: The largest term (3,000) is close to 3,456, which makes sense. The sum 3,000 + 400 + 50 + 6 = 3,456 confirms the answer is correct!