Solved Exercises on Expanded Form of Numbers in Grade 4

Master expanded form of numbers: place value decomposition, standard to expanded conversion, addition using expanded form through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Place Value Decomposition
Exercise 1
Write 3,456 in expanded form using place value.
Definition:

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

Place value method:
  1. Identify the place value of each digit
  2. Write each digit with its place value
  3. Add all parts together
Standard Form
3,456
Expanded Form
3,000 + 400 + 50 + 6
Step 1: Identify place values

3,456 has digits in these places:

  • 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 each digit with its place value

3,000 + 400 + 50 + 6

Step 3: Verify the sum equals original number

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 position represents a power of 10

• Digit Multiplication: Each digit is multiplied by its place value

• Addition: All parts are added together to form the number

2 Converting Standard to Expanded
Exercise 2
Convert 7,284 to expanded form.
Definition:

Standard to expanded conversion: Breaking down a number by its place value positions.

Standard Form
7,284
Expanded Form
7,000 + 200 + 80 + 4
Step 1: Identify each digit and its place value

7,284 breakdown:

  • 7 is in thousands place: 7 × 1,000 = 7,000
  • 2 is in hundreds place: 2 × 100 = 200
  • 8 is in tens place: 8 × 10 = 80
  • 4 is in ones place: 4 × 1 = 4
Step 2: Write expanded form

7,000 + 200 + 80 + 4

Step 3: Verify by adding

7,000 + 200 + 80 + 4 = 7,284 ✓

7,284 = 7,000 + 200 + 80 + 4
Final answer:

7,284 = 7,000 + 200 + 80 + 4

Applied rules:

• Place Value Recognition: Know thousands, hundreds, tens, ones

• Multiplication: Multiply each digit by its place value

• Verification: Check that the sum equals the original number

3 Working with Zeros
Exercise 3
Write 5,070 in expanded form.
Definition:

Handling zeros in expanded form: Even zeros have place values, but their contribution is zero.

Standard Form
5,070
Expanded Form
5,000 + 0 + 70 + 0
Simplified
5,000 + 70
Step 1: Identify each digit and its place value

5,070 breakdown:

  • 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
  • 0 is in ones place: 0 × 1 = 0
Step 2: Write full expanded form

5,000 + 0 + 70 + 0

Step 3: Simplify by removing zeros

5,000 + 70

Step 4: Verify

5,000 + 70 = 5,070 ✓

5,070 = 5,000 + 70
Final answer:

5,070 = 5,000 + 70

Applied rules:

• Zero Rule: Zeros still hold place value but contribute nothing to the sum

• Simplification: Zero terms can be omitted in final answer

• Verification: Always check the sum equals original number

Rules and methods, laws,...
4,523 = 4,000 + 500 + 20 + 3
Expanded Form
Thousands
Digit × 1,000
First position from left
Hundreds
Digit × 100
Second position from left
Tens
Digit × 10
Third position from left
Ones
Digit × 1
Rightmost position
Key definitions:

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

Standard Form: The normal way we write numbers (e.g., 1,234)

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

Complete methodology:
  1. Identify digits: Look at each digit in the number
  2. Determine place values: Know thousands, hundreds, tens, ones
  3. Multiply: Multiply each digit by its place value
  4. Add: Combine all parts with addition
  5. Verify: Check that the sum equals the original number
Tip 1: Remember the place values: Thousands, Hundreds, Tens, Ones (THHO).
Tip 2: Zeros in expanded form contribute nothing but still hold their place value.
Tip 3: Always verify by adding the expanded parts to get the original number.
Common errors: Forgetting to multiply digits by their place values, misidentifying place values, omitting zeros incorrectly.
Key note: Expanded form helps understand the actual value each digit contributes to the whole number.
Formulas to know by heart:

• Standard to Expanded: abcd = a×1000 + b×100 + c×10 + d×1

• Place Values: Thousands (1000), Hundreds (100), Tens (10), Ones (1)

• Zero Rule: Any digit × 0 = 0, but zero digits still hold their place value

Solution: Exercises 4 to 5
4 Addition Using Expanded Form
Exercise 4
Add 2,456 and 1,378 using expanded form.
Definition:

Addition using expanded form: Break down each number, add like place values, then combine.

Step 1
2,456 = 2,000 + 400 + 50 + 6
Step 2
1,378 = 1,000 + 300 + 70 + 8
Step 3
3,834 = 3,000 + 700 + 120 + 14
Step 1: Write each number in expanded form

2,456 = 2,000 + 400 + 50 + 6

1,378 = 1,000 + 300 + 70 + 8

Step 2: Add like place values together

Thousands: 2,000 + 1,000 = 3,000

Hundreds: 400 + 300 = 700

Tens: 50 + 70 = 120

Ones: 6 + 8 = 14

Step 3: Combine and simplify if needed

3,000 + 700 + 120 + 14 = 3,834

Step 4: Verify by standard addition

2,456 + 1,378 = 3,834 ✓

2,456 + 1,378 = 3,834
Final answer:

2,456 + 1,378 = 3,834

Applied rules:

• Like Terms: Only add digits with the same place value

• Regrouping: When sums exceed place value limits, carry over

• Verification: Always check with standard addition

5 Comparing Numbers Using Expanded Form
Exercise 5
Compare 4,521 and 4,512 using expanded form to determine which is larger.
Definition:

Comparing using expanded form: Compare numbers by examining each place value from left to right.

Number 1
4,521 = 4,000 + 500 + 20 + 1
Number 2
4,512 = 4,000 + 500 + 10 + 2
Comparison
4,521 > 4,512
Step 1: Write both numbers in expanded form

4,521 = 4,000 + 500 + 20 + 1

4,512 = 4,000 + 500 + 10 + 2

Step 2: Compare place values from left to right

Thousands: 4,000 = 4,000 (equal)

Hundreds: 500 = 500 (equal)

Tens: 20 > 10 (4,521 has more tens)

Therefore: 4,521 > 4,512

Step 3: Make the comparison

Since 20 > 10 in the tens place, 4,521 is greater

Step 4: Verify by standard comparison

4,521 > 4,512 ✓

4,521 > 4,512
Final answer:

4,521 is greater than 4,512

Applied rules:

• Left-to-Right Comparison: Start with highest place value

• Place Value Priority: Higher place values determine the relationship

• First Difference: The first differing place value determines the outcome

Place Value and Expanded Form: Complete Guide
abcde = a×10,000 + b×1,000 + c×100 + d×10 + e×1
Expanded Form Formula
Key definitions:

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

Standard Form: The normal way we write numbers (e.g., 1,234)

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

Regrouping: Carrying over when a place value exceeds its limit

Complete methodology:
  1. Identify the number: Look at the given number
  2. Recognize place values: Know thousands, hundreds, tens, ones
  3. Break down digits: Separate each digit with its position
  4. Multiply by place value: Each digit × its place value
  5. Add components: Sum all parts with addition signs
  6. Verify: Check that the sum equals the original number
Tip 1: Use the acronym THHO (Thousands, Hundreds, Tens, Ones) to remember place values.
Tip 2: Draw a place value chart to visualize the positions.
Tip 3: Always verify by adding the expanded parts to ensure accuracy.
Tip 4: Practice with numbers containing zeros to master the concept completely.
Common errors: Forgetting to multiply by place value, misidentifying place positions, incorrect handling of zeros.
Exam preparation: Practice converting between standard and expanded forms, work with various place values.
Formulas to know by heart:

• Standard to Expanded: abcd = a×1000 + b×100 + c×10 + d×1

• Place Values: Thousands (1000), Hundreds (100), Tens (10), Ones (1)

• Zero Handling: Zeros contribute 0 but maintain their place value position

• Verification: Always check that expanded parts sum to original number

Exercise with Visualization: Place Value Relationships
Exercise 6: Place Value Charts
Consider the following numbers and their expanded forms:
2,456 = 2,000 + 400 + 50 + 6
3,789 = 3,000 + 700 + 80 + 9
5,024 = 5,000 + 0 + 20 + 4

Analysis: The chart shows how each digit contributes to the total value based on its position.

  • 2,456: Thousands (2,000), Hundreds (400), Tens (50), Ones (6)
  • 3,789: Thousands (3,000), Hundreds (700), Tens (80), Ones (9)
  • 5,024: Thousands (5,000), Hundreds (0), Tens (20), Ones (4)

Questions & Answers

Question: I don't understand why we need to learn expanded form. Isn't it just extra work?

Answer: Great question! Expanded form is incredibly important because:

  • It helps you understand what each digit actually means in a number
  • It builds a strong foundation for addition, subtraction, and regrouping
  • It makes comparing numbers easier when you see their components
  • It prepares you for working with larger numbers and decimals later

For example, when you see 5,432 = 5,000 + 400 + 30 + 2, you understand that the 5 represents five thousand, not just 5. This understanding is crucial for all future math!

Think of it like taking apart a toy to see how it works - expanded form shows you how numbers are built!

Question: When I have a number like 3,040, how do I handle the zeros in expanded form?

Answer: With zeros in expanded form, you have two approaches:

  • Full form: 3,040 = 3,000 + 0 + 40 + 0 (shows all place values)
  • Simplified form: 3,040 = 3,000 + 40 (omit zero contributions)

Both are correct! The full form helps you see that the hundreds and ones places exist but contain zero value. The simplified form is more concise and commonly used.

Remember: zeros still hold their place in the number structure, even though they contribute nothing to the total value.

Example: In 3,040, the zero in the hundreds place tells us there are no hundreds, but it maintains the position for the thousands and tens.

Question: How can I remember the order of place values? I keep mixing up thousands, hundreds, tens, and ones.

Answer: Here are effective memory tricks for place values:

  • Acronym: Use THHO = Thousands, Hundreds, Tens, Ones
  • Visual: Think of the number line going from biggest (left) to smallest (right)
  • Counting: Say "Thousand, Hundred, Ten, One" while pointing from left to right
  • Practice: Write numbers and label each digit with its place value

Another helpful method is to think about the number of zeros in each place value:

  • Thousands: 3 zeros (1,000)
  • Hundreds: 2 zeros (100)
  • Tens: 1 zero (10)
  • Ones: 0 zeros (1)

Practice with many examples until the pattern becomes automatic!

Question: How can I check if my expanded form is correct?

Answer: The most reliable method to verify expanded form is to add all the parts together and see if you get back to the original number.

For example, if you wrote 4,523 = 4,000 + 500 + 20 + 3, add: 4,000 + 500 + 20 + 3 = 4,523 ✓

Additional verification methods:

  • Count the number of digits in your expanded form parts
  • Check that each digit appears in the correct place value position
  • Use estimation to see if the expanded parts make sense

This verification technique is especially important for catching mistakes with zeros and place values.

Question: What is the best strategy to convert large numbers to expanded form quickly?

Answer: Here's a systematic approach for large numbers:

  1. Read the number aloud: "Five thousand, two hundred thirty-four"
  2. Identify each digit's position: 5 is thousands, 2 is hundreds, etc.
  3. Write the multiplication: 5×1000, 2×100, 3×10, 4×1
  4. Calculate each part: 5000, 200, 30, 4
  5. Combine with addition: 5000 + 200 + 30 + 4

Practice this process with many examples until it becomes automatic. The key is recognizing the pattern of place values.

For numbers with zeros, still identify the place value even if the digit is zero!