Solved Exercises on Expanded Form Numbers in Grade 4

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

Solution: Exercises 1 to 3
1 Place Value Decomposition
Exercise 1
Write 5,482 in expanded form.
Definition:

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

Method:
  1. Identify the place value of each digit
  2. Multiply each digit by its place value
  3. Write the sum of these products
Number
5,482
Expanded
5,000 + 400 + 80 + 2
Step 1: Identify place values

5 is in thousands place (5,000), 4 is in hundreds place (400), 8 is in tens place (80), 2 is in ones place (2)

Step 2: Multiply each digit by its place value

5 × 1,000 = 5,000; 4 × 100 = 400; 8 × 10 = 80; 2 × 1 = 2

Step 3: Write the sum

5,482 = 5,000 + 400 + 80 + 2

5,482 = 5,000 + 400 + 80 + 2
Final answer:

5,482 = 5,000 + 400 + 80 + 2

Applied rules:

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

• Digit interpretation: A digit's value depends on its position

• Addition principle: Sum of place values equals the original number

2 Multi-digit Analysis
Exercise 2
Write 12,345 in expanded form.
Definition:

Place value positions: Ones, tens, hundreds, thousands, ten-thousands, hundred-thousands...

Number
12,345
Expanded
10,000 + 2,000 + 300 + 40 + 5
Step 1: Identify place values

1 is in ten-thousands place (10,000), 2 is in thousands place (2,000), 3 is in hundreds place (300), 4 is in tens place (40), 5 is in ones place (5)

Step 2: Multiply each digit by its place value

1 × 10,000 = 10,000; 2 × 1,000 = 2,000; 3 × 100 = 300; 4 × 10 = 40; 5 × 1 = 5

Step 3: Write the sum

12,345 = 10,000 + 2,000 + 300 + 40 + 5

12,345 = 10,000 + 2,000 + 300 + 40 + 5
Final answer:

12,345 = 10,000 + 2,000 + 300 + 40 + 5

Applied rules:

• Place value progression: Each position is 10 times the previous position

• Digit positioning: Reading numbers from left to right determines place value

• Decimal system: Our number system is base 10

3 Zero Placeholders
Exercise 3
Write 40,507 in expanded form.
Definition:

Zero placeholders: Zeros in a number still represent their place value (even though the digit is 0)

Number
40,507
Expanded
40,000 + 0 + 500 + 0 + 7
Simplified
40,000 + 500 + 7
Step 1: Identify place values

4 is in ten-thousands place (40,000), 0 is in thousands place (0), 5 is in hundreds place (500), 0 is in tens place (0), 7 is in ones place (7)

Step 2: Multiply each digit by its place value

4 × 10,000 = 40,000; 0 × 1,000 = 0; 5 × 100 = 500; 0 × 10 = 0; 7 × 1 = 7

Step 3: Write the sum

40,507 = 40,000 + 0 + 500 + 0 + 7 = 40,000 + 500 + 7

Step 4: Simplify (optional)

We can omit the zero terms: 40,000 + 500 + 7

40,507 = 40,000 + 500 + 7
Final answer:

40,507 = 40,000 + 500 + 7

Applied rules:

• Zero representation: Even though 0×value=0, zeros hold place value

• Position significance: Every position matters for number value

• Simplification rule: We can omit terms with 0 coefficients

Rules and methods, laws,...
abcde = a×10,000 + b×1,000 + c×100 + d×10 + e×1
Expanded Form Formula
Ones Place
digit × 1
Rightmost digit
Tens Place
digit × 10
Second from right
Hundreds Place
digit × 100
Third from right
Thousands Place
digit × 1,000
Fourth from right
Ten-Thousands Place
digit × 10,000
Fifth from right
Key definitions:

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

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

Standard form: The usual way we write numbers (like 5,482)

Complete methodology:
  1. Identify positions: Starting from the right, identify the place value of each digit
  2. Multiply digits: Multiply each digit by its corresponding place value
  3. Sum results: Add all the products together
  4. Verify: Check that the expanded form equals the original number
Tip 1: Remember: Ones, Tens, Hundreds, Thousands, Ten-Thousands...
Tip 2: Each place value is 10 times the one to its right.
Tip 3: Zeros in the middle of numbers still represent their place value.
Tip 4: Always check your work by adding the expanded parts.
Common errors: Forgetting to include zero place values, misidentifying place values, confusing expanded and standard form.
Key concepts: Understanding that each position represents a power of 10 (1, 10, 100, 1000, etc.).
Formulas to know by heart:

• Place value pattern: Each position is 10 times the previous position

• Expanded form: Sum of each digit multiplied by its place value

• Verification: Adding expanded parts should equal original number

Solution: Exercises 4 to 5
4 Converting Expanded to Standard Form
Exercise 4
Write the standard form of 7,000 + 500 + 30 + 2
Definition:

Standard form: The usual way of writing numbers (without showing place values)

Expanded
7,000 + 500 + 30 + 2
Standard
7,532
Step 1: Add the values

7,000 + 500 + 30 + 2 = 7,532

Step 2: Verify the place values

7 is in thousands place, 5 is in hundreds place, 3 is in tens place, 2 is in ones place

Step 3: Confirm the conversion

Expanded form 7,000 + 500 + 30 + 2 equals standard form 7,532

7,000 + 500 + 30 + 2 = 7,532
Final answer:

7,000 + 500 + 30 + 2 = 7,532

Applied rules:

• Addition principle: Sum of expanded parts equals standard form

• Place value recognition: Each part corresponds to a specific position

• Verification: Convert back to expanded form to check accuracy

5 Complex Number Decomposition
Exercise 5
Write 234,567 in expanded form.
Definition:

Large number decomposition: Extending place value concept to higher positions (hundred-thousands, millions, etc.)

Number
234,567
Expanded
200,000 + 30,000 + 4,000 + 500 + 60 + 7
Step 1: Identify place values

2 is in hundred-thousands place (200,000), 3 is in ten-thousands place (30,000), 4 is in thousands place (4,000), 5 is in hundreds place (500), 6 is in tens place (60), 7 is in ones place (7)

Step 2: Multiply each digit by its place value

2 × 100,000 = 200,000; 3 × 10,000 = 30,000; 4 × 1,000 = 4,000; 5 × 100 = 500; 6 × 10 = 60; 7 × 1 = 7

Step 3: Write the sum

234,567 = 200,000 + 30,000 + 4,000 + 500 + 60 + 7

Step 4: Verify the result

Add: 200,000 + 30,000 + 4,000 + 500 + 60 + 7 = 234,567 ✓

234,567 = 200,000 + 30,000 + 4,000 + 500 + 60 + 7
Final answer:

234,567 = 200,000 + 30,000 + 4,000 + 500 + 60 + 7

Applied rules:

• Place value continuation: Pattern continues beyond thousands (ten-thousands, hundred-thousands)

• Systematic approach: Work from left to right, identifying each position

• Verification: Always check by adding the expanded parts

Comprehensive Guide: Laws, Methods, Rules, Definitions
abcde = a×10,000 + b×1,000 + c×100 + d×10 + e×1
Expanded Form Formula
Key definitions:

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

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

Standard form: The usual way we write numbers (like 5,482)

Base 10 system: Our number system where each position is 10 times the previous position

Complete methodology:
  1. Analyze the number: Count the digits and identify the highest place value
  2. Identify positions: From right to left, determine each digit's place value (ones, tens, hundreds...)
  3. Multiply digits: Multiply each digit by its corresponding place value
  4. Write the sum: Express the number as addition of all the products
  5. Verify: Add the expanded parts to ensure they equal the original number
Tip 1: Remember the sequence: Ones, Tens, Hundreds, Thousands, Ten-Thousands, Hundred-Thousands...
Tip 2: Each place value is 10 times the one to its right (10×1=10, 10×10=100, etc.)
Tip 3: Zeros in the middle of numbers still represent their place value (40,507 = 40,000 + 500 + 7)
Tip 4: Always check your work by adding the expanded parts to verify they equal the original number
Common errors: Forgetting to include zero place values, misidentifying place values, confusing expanded and standard form, skipping positions with zeros.
Exam preparation: Practice with various numbers, pay attention to zeros, memorize place value names, understand the base 10 system.
Formulas to know by heart:

• Place value pattern: Each position is 10 times the previous position

• Expanded form: Sum of each digit multiplied by its place value

• Verification: Adding expanded parts should equal original number

• Base 10 relationship: 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand, etc.

Exercise with Visualization: Place Value Relationships
Exercise 6: Place Value Patterns
Consider the following numbers and their expanded forms:
123 = 100 + 20 + 3
1,234 = 1,000 + 200 + 30 + 4
12,345 = 10,000 + 2,000 + 300 + 40 + 5

Analysis: The chart shows how each digit's contribution to the total number increases by powers of 10 as we move left.

  • 123 = 100 + 20 + 3 (1×100 + 2×10 + 3×1)
  • 1,234 = 1,000 + 200 + 30 + 4 (1×1000 + 2×100 + 3×10 + 4×1)
  • 12,345 = 10,000 + 2,000 + 300 + 40 + 5 (1×10000 + 2×1000 + 3×100 + 4×10 + 5×1)

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 helps you understand how our number system works:

  • It shows you that each digit has a different value based on its position
  • It builds your understanding of place value, which is essential for addition, subtraction, multiplication, and division
  • It helps you compare large numbers more easily
  • It prepares you for working with decimals later

Think of it like understanding how money works: $54.82 means 5 tens ($50) + 4 ones ($4) + 8 tenths (80¢) + 2 hundredths (2¢). Expanded form teaches you the same concept with whole numbers!

Understanding place value makes all math easier and more logical!

Question: When I have a number like 305, how do I handle the zero in the tens place? Should I write 0 in the expanded form?

Answer: Excellent observation! Here's how to handle zeros in expanded form:

  • You can write it as: 305 = 300 + 0 + 5 (showing the zero tens)
  • Or you can simplify it to: 305 = 300 + 5 (omitting the zero tens)

Both are correct! The zero in 305 holds the tens place, which tells us there are no tens in the number. In expanded form, the zero reminds us that the 3 is in the hundreds place and the 5 is in the ones place.

For learning purposes, writing "300 + 0 + 5" helps reinforce that the zero is holding the tens place. Later, you can simplify to "300 + 5" once you understand the concept.

Remember: the zero doesn't change the value, but it's important for the place value structure!

Question: I have trouble remembering the names of all the place values. Is there a trick to remember them?

Answer: Yes! Here are some helpful tricks for remembering place values:

  • Count from right to left: Start with "ones" (rightmost), then "tens", "hundreds", "thousands", "ten-thousands", "hundred-thousands"
  • Grouping method: Think in groups of 3: Units (ones, tens, hundreds), Thousands (thousands, ten-thousands, hundred-thousands)
  • Memory phrase: "Ones, Tens, Hundreds - that's how the count goes! Then Thousands, Ten-Thousands, Hundred-Thousands - those come next!"
  • Visual pattern: Each place value is 10 times bigger than the one before it

Another way to remember: the "s" at the end changes - "one" becomes "tens", "ten" becomes "hundreds", "hundred" becomes "thousands".

Practice with different numbers regularly - the more you work with place values, the more natural they'll become!