Solved Exercises on Number Form and Expanded Form in Grade 4

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

Solution: Exercises 1 to 3
1 Basic number form and expanded form
Exercise 1
Write the number 5,728 in standard form and expanded form.
Definition:

Standard form: The regular way we write numbers (e.g., 5,728)

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

Conversion Method:
  1. Standard form is already given: 5,728
  2. Identify the place value of each digit
  3. Write each digit multiplied by its place value
  4. Join all parts with addition signs
Standard Form
5,728
Expanded Form
5,000 + 700 + 20 + 8
Step 1: Identify place values

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

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

5,728 = 5,000 + 700 + 20 + 8

Step 3: Verify the calculation

5,000 + 700 + 20 + 8 = 5,728 ✓

Standard Form: 5,728
Expanded Form: 5,000 + 700 + 20 + 8
Final answer:

Standard Form: 5,728

Expanded Form: 5,000 + 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 Number form and expanded form with zeros
Exercise 2
Write 8,053 in standard form and expanded form.
Definition:

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

Standard Form
8,053
Expanded Form
8,000 + 0 + 50 + 3
Simplified
8,000 + 50 + 3
Step 1: Identify place values

8 is in thousands place: 8 × 1,000 = 8,000

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

8,053 = 8,000 + 0 + 50 + 3

Step 3: Simplify by omitting zero terms

8,053 = 8,000 + 50 + 3

Step 4: Verify the calculation

8,000 + 50 + 3 = 8,053 ✓

Standard Form: 8,053
Expanded Form: 8,000 + 50 + 3
Final answer:

Standard Form: 8,053

Expanded Form: 8,000 + 50 + 3

Applied rules:

• Zero Inclusion: Zeros are written as their place value

• Simplification: Terms with 0 can be omitted

• Verification: Sum of parts equals original number

3 Converting expanded form to standard form
Exercise 3
What number is represented by 40,000 + 5,000 + 0 + 60 + 2?
Definition:

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

Expanded Form
40,000 + 5,000 + 0 + 60 + 2
Standard Form
45,062
Step 1: Add all parts of the expanded form

40,000 + 5,000 + 0 + 60 + 2 = 45,062

Step 2: Verify by converting back to expanded form

45,062 = 40,000 + 5,000 + 0 + 60 + 2 ✓

40,000 + 5,000 + 0 + 60 + 2 = 45,062
Final answer:

The number is 45,062

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

Number Form and Expanded Form Rules
\(5,728 = 5,000 + 700 + 20 + 8\)
Number Form and 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
Ten-Thousands Place
\(d \times 10,000\)
Digit × 10,000
Key definitions:

Standard Form: The regular way we write numbers (e.g., 5,728)

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

Word Form: Writing numbers using words (e.g., five thousand seven hundred twenty-eight)

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

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

Complete methodology:
  1. Identify positions: Recognize place values (ones, tens, hundreds, thousands, etc.)
  2. Write multiplication: Express each digit as (digit × place value)
  3. Join with addition: Combine all parts with plus signs
  4. Verify: Check that the sum equals the original number
Tip 1: Remember the place value pattern: 1, 10, 100, 1,000, 10,000...
Tip 2: Zeros in expanded form can be written as their place value or omitted.
Tip 3: Always verify by adding the expanded form 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 standard form with expanded 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 Comparing number forms
Exercise 4
Write 6,482 in standard form, expanded form, and word form.
Definition:

Multiple number forms: Same number shown in different mathematical forms

Standard Form
6,482
Expanded Form
6,000 + 400 + 80 + 2
Word Form
Six thousand four hundred eighty-two
Step 1: Identify place values for expanded form

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

4 is in hundreds place: 4 × 100 = 400

8 is in tens place: 8 × 10 = 80

2 is in ones place: 2 × 1 = 2

Step 2: Write in expanded form

6,482 = 6,000 + 400 + 80 + 2

Step 3: Write in word form

6,482 = Six thousand four hundred eighty-two

Step 4: Verify all forms are equivalent

6,000 + 400 + 80 + 2 = 6,482 ✓

Standard Form: 6,482
Expanded Form: 6,000 + 400 + 80 + 2
Word Form: Six thousand four hundred eighty-two
Final answer:

Standard Form: 6,482

Expanded Form: 6,000 + 400 + 80 + 2

Word Form: Six thousand four hundred eighty-two

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

5 Converting between forms
Exercise 5
If a number in expanded form is 30,000 + 7,000 + 0 + 40 + 9, write it in standard form and word form.
Definition:

Conversion between forms: Changing from one representation to another

Expanded Form
30,000 + 7,000 + 0 + 40 + 9
Standard Form
37,049
Word Form
Thirty-seven thousand forty-nine
Step 1: Add all parts of the expanded form

30,000 + 7,000 + 0 + 40 + 9 = 37,049

Step 2: Write in standard form

37,049

Step 3: Write in word form

37,049 = Thirty-seven thousand forty-nine

Step 4: Verify by converting back to expanded form

37,049 = 30,000 + 7,000 + 0 + 40 + 9 ✓

Expanded Form: 30,000 + 7,000 + 0 + 40 + 9
Standard Form: 37,049
Word Form: Thirty-seven thousand forty-nine
Final answer:

Standard Form: 37,049

Word Form: Thirty-seven thousand forty-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: Number Form and Expanded Form
\(d_n \times 10^n + d_{n-1} \times 10^{n-1} + ... + d_1 \times 10^1 + d_0 \times 10^0\)
General Expanded Form Formula
Key definitions:

Standard Form: The usual way we write numbers (e.g., 5,728)

Expanded Form: A number expressed as the sum of each digit's place value

Word Form: Writing numbers using words (e.g., five thousand seven hundred twenty-eight)

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

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

Number Forms: Different ways to represent the same number

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 for expanded form
  4. Verification: Add the expanded form 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 extending.
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 number forms, 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

• Number Forms: Standard, Expanded, Word

Number Form Visualization: Different Representations
Exercise 6: Understanding Number Forms
Consider the following number and its different forms:
Standard: 4,567
Expanded: 4,000 + 500 + 60 + 7
Word: Four thousand five hundred sixty-seven

Analysis: The chart shows how the same number can be represented in different forms.

  • Standard Form: 4,567 (Four thousand five hundred sixty-seven)
  • Expanded Form: 4,000 + 500 + 60 + 7 (Four thousands + Five hundreds + Six tens + Seven ones)
  • Word Form: Four thousand five hundred sixty-seven

Questions & Answers

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

Answer: Great question! Learning different number forms is crucial for understanding how our number system works:

  • It helps you understand what each digit means in a number
  • 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
  • It shows the relationship between digits and their place values
  • It helps with reading and writing numbers in different contexts

For example, in expanded form (5,000 + 700 + 20 + 8), you can see that the 5 represents 5 thousands (5,000), not just 5. This helps you understand the true value of each digit!

Question: My child gets confused when there are zeros in the expanded form like 8,053 = 8,000 + 0 + 50 + 3. How do I explain this?

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

  • In 8,053 = 8,000 + 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 8,053: 8 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 8,000 + 50 + 3, but including the zero version shows the complete place value structure.

Question: What's the difference between expanded form and standard form? How do I convert between them?

Answer: Here's how to understand and convert between forms:

  • Standard Form: Shows the number in its regular format (e.g., 5,728)
  • Expanded Form: Shows each digit's place value (e.g., 5,000 + 700 + 20 + 8)
  • Converting Standard to Expanded: Break apart each digit by its place value
  • Converting Expanded to Standard: Add all the parts together

Standard Form: 5,728

Expanded Form: 5,000 + 700 + 20 + 8

To convert from expanded to standard: 5,000 + 700 + 20 + 8 = 5,728

To convert from standard to expanded: Look at each digit and multiply by its place value!