Solved Exercises on Expanded Form and Number Names in Grade 4

Master expanded form and number names: place value, standard form, word form, and base ten through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Expanded form conversion
Exercise 1
Write 5,327 in expanded form.
Definition:

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

Expanded form method:
  1. Identify each digit and its place value (thousands, hundreds, tens, ones)
  2. Multiply each digit by its place value
  3. Add all parts together
Standard Form
5,327
Expanded Form
5,000 + 300 + 20 + 7
Step 1: Identify place values

5,327 has digits: 5 (thousands), 3 (hundreds), 2 (tens), 7 (ones)

Step 2: Multiply each digit by its place value

5 × 1,000 = 5,000; 3 × 100 = 300; 2 × 10 = 20; 7 × 1 = 7

Step 3: Add all parts together

5,000 + 300 + 20 + 7 = 5,327

5,327 = 5,000 + 300 + 20 + 7
Final answer:

5,327 = 5,000 + 300 + 20 + 7

Applied rules:

• Place Value: Each position represents a power of 10

• Expanded Form: Sum of digits multiplied by their place values

• Verification: Add expanded parts to get original number

2 Number names conversion
Exercise 2
Write 8,456 in number names.
Definition:

Number names: Writing numbers using words instead of digits.

Standard Form
8,456
Number Names
Eight thousand four hundred fifty-six
Step 1: Identify thousands place

8 in thousands place = Eight thousand

Step 2: Identify remaining digits

456 = Four hundred fifty-six

Step 3: Combine with comma separator

Eight thousand, four hundred fifty-six

8,456 = Eight thousand four hundred fifty-six
Final answer:

8,456 = Eight thousand four hundred fifty-six

Applied rules:

• Comma Rule: Use commas to separate periods (thousands)

• Hyphenation: Hyphenate compound numbers from 21-99 except multiples of 10

• Conjunction: Use "and" only when separating whole numbers from decimals

3 Mixed conversion
Exercise 3
Convert 7,082 to expanded form and number names.
Definition:

Place value system: Each position represents a power of 10, with zeros holding empty places.

Standard Form
7,082
Expanded Form
7,000 + 0 + 80 + 2
Number Names
Seven thousand eighty-two
Step 1: Identify place values

7,082 has digits: 7 (thousands), 0 (hundreds), 8 (tens), 2 (ones)

Step 2: Write expanded form

7 × 1,000 = 7,000; 0 × 100 = 0; 8 × 10 = 80; 2 × 1 = 2

7,000 + 0 + 80 + 2 = 7,082

Step 3: Write number names

7 thousand = Seven thousand; 82 = eighty-two

Seven thousand eighty-two

7,082 = 7,000 + 80 + 2 = Seven thousand eighty-two
Final answer:

Expanded: 7,000 + 80 + 2

Number names: Seven thousand eighty-two

Applied rules:

• Zero Rule: Zeros in middle positions are omitted in number names

• Place Value: Even zero digits contribute to expanded form

• Word Formation: Compound numbers like eighty-two are hyphenated

Rules and methods, laws,...
Standard Form = Expanded Form = Number Names
Number Conversion System
Expanded Form
5,327 = 5,000 + 300 + 20 + 7
Sum of place values
Number Names
5,327 = Five thousand three hundred twenty-seven
Words instead of digits
Place Values
Thousands, Hundreds, Tens, Ones
Position-based values
Key definitions:

Standard Form: Writing numbers with digits (e.g., 4,567)

Expanded Form: Writing numbers as the sum of each digit multiplied by its place value

Number Names: Writing numbers using words instead of digits

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

Complete methodology:
  1. Identify the number: Recognize the standard form and digit positions
  2. Apply place values: Understand thousands, hundreds, tens, and ones
  3. Convert to expanded form: Multiply each digit by its place value
  4. Convert to number names: Write out each period with proper grammar
Tip 1: Remember the place value chart: Thousands, Hundreds, Tens, Ones.
Tip 2: In number names, hyphenate compound numbers from 21-99 except multiples of 10.
Tip 3: When converting to expanded form, include zeros even if they're in the middle.
Tip 4: Always verify your work by adding expanded parts to get the original number.
Common errors: Forgetting place values, misreading zeros, incorrect hyphenation in number names.
Exam preparation: Practice with numbers up to 9,999, memorize place values, learn number name patterns.
Formulas to know by heart:

• Place Value Pattern: Thousands (1,000), Hundreds (100), Tens (10), Ones (1)

• Expanded Form: Number = Digit × Place Value + Digit × Place Value...

• Number Name Rules: Hyphenate 21-99 except multiples of 10, use commas for thousands

• Zero Handling: Include zeros in expanded form, omit in number names when in middle positions

Solution: Exercises 4 to 5
4 Word to standard form
Exercise 4
Write "Three thousand two hundred forty-five" in standard form and expanded form.
Definition:

Word form to standard form: Converting number names back to digits using place value understanding.

Number Names
Three thousand two hundred forty-five
Standard Form
3,245
Expanded Form
3,000 + 200 + 40 + 5
Step 1: Identify thousands period

"Three thousand" means 3 in the thousands place: 3,___

Step 2: Identify remaining period

"Two hundred forty-five" means 2 in hundreds, 4 in tens, 5 in ones: 3,245

Step 3: Write expanded form

3 × 1,000 = 3,000; 2 × 100 = 200; 4 × 10 = 40; 5 × 1 = 5

3,000 + 200 + 40 + 5

Step 4: Verify the result

3,000 + 200 + 40 + 5 = 3,245 ✓

Three thousand two hundred forty-five = 3,245 = 3,000 + 200 + 40 + 5
Final answer:

Standard form: 3,245

Expanded form: 3,000 + 200 + 40 + 5

Applied rules:

• Period Recognition: Identify thousands period and remaining digits separately

• Place Value Mapping: Map words to specific place values

• Verification: Always check by converting back to original form

5 Multi-step conversion
Exercise 5
Convert 9,050 to expanded form, then write that expanded form in number names.
Definition:

Multi-step conversion: Performing multiple conversions sequentially while maintaining accuracy.

Original Number
9,050
Expanded Form
9,000 + 0 + 50 + 0
Final Answer
Nine thousand fifty
Step 1: Identify place values in 9,050

9 (thousands), 0 (hundreds), 5 (tens), 0 (ones)

Step 2: Write expanded form

9 × 1,000 = 9,000; 0 × 100 = 0; 5 × 10 = 50; 0 × 1 = 0

9,000 + 0 + 50 + 0

Step 3: Convert expanded form to number names

Since we have 9,000 and 50, combine as "Nine thousand fifty"

Note: Omit "zero hundreds" and "zero ones" in number names

Step 4: Verify the result

9,000 + 50 = 9,050 ✓

9,050 → 9,000 + 50 → Nine thousand fifty
Final answer:

Expanded form: 9,000 + 50

Number names: Nine thousand fifty

Applied rules:

• Zero Omission: Omit zeros when converting to number names

• Sequential Processing: Complete one conversion before starting the next

• Verification: Check final result against original number

Expanded Form and Number Names Guide
Standard Form ↔ Expanded Form ↔ Number Names
Conversion Relationships
Key definitions:

Standard Form: Writing numbers with digits (e.g., 4,567)

Expanded Form: Writing numbers as the sum of each digit multiplied by its place value

Number Names: Writing numbers using words instead of digits

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

Complete methodology:
  1. Analyze the number: Recognize the structure and identify place values
  2. Choose the conversion: Standard to expanded, expanded to number names, etc.
  3. Apply the method: Follow the steps for the chosen conversion
  4. Verify the result: Check by converting back to original form
Tip 1: Use place value charts to organize digits: THOUSANDS | HUNDREDS | TENS | ONES
Tip 2: In number names, always hyphenate compound numbers from 21-99 (twenty-one, thirty-five).
Tip 3: When converting to expanded form, include every place value including zeros.
Tip 4: Always check your work by adding expanded parts to ensure they equal the original number.
Common errors: Forgetting place values, misreading zeros, incorrect hyphenation in number names.
Exam preparation: Practice with numbers up to 9,999, memorize place values, learn number name patterns.
Formulas to know by heart:

• Place Value Pattern: Thousands (1,000), Hundreds (100), Tens (10), Ones (1)

• Expanded Form: Number = Digit × Place Value + Digit × Place Value...

• Number Name Rules: Hyphenate 21-99 except multiples of 10, use commas for thousands

• Zero Handling: Include zeros in expanded form, omit in number names when in middle positions

Visual Representation: Place Value System
Place Value Visualization
Consider the number 4,729 and its representations:
Standard Form: 4,729
Expanded Form: 4,000 + 700 + 20 + 9
Number Names: Four thousand seven hundred twenty-nine

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

  • 4 in thousands place = 4 × 1,000 = 4,000
  • 7 in hundreds place = 7 × 100 = 700
  • 2 in tens place = 2 × 10 = 20
  • 9 in ones place = 9 × 1 = 9
  • Total: 4,000 + 700 + 20 + 9 = 4,729

Questions & Answers

Question: I don't understand why we write 5,040 as "Five thousand forty" and not "Five thousand zero forty". Why do we skip the zero in the hundreds place?

Answer: Great observation! This is an important rule in number names:

  • In number names, we only say the non-zero digits along with their place values
  • When a place value (like hundreds or tens) has a zero, we skip mentioning that place entirely
  • This makes the number names cleaner and easier to say

For 5,040:

  • 5 in thousands place = Five thousand
  • 0 in hundreds place = We skip this
  • 4 in tens place = Forty
  • 0 in ones place = We skip this

So the number name is "Five thousand forty". However, in expanded form, we still include the zero: 5,000 + 0 + 40 + 0.

Question: When I write expanded form, do I always need to include the zeros? Like for 3,050, should I write 3,000 + 0 + 50 + 0?

Answer: Yes, you should include the zeros in expanded form! Here's why:

  • Expanded form shows ALL place values, even when they're zero
  • This helps you understand the complete structure of the number
  • It maintains the relationship between each digit and its place value

For 3,050:

  • 3 in thousands place = 3,000
  • 0 in hundreds place = 0 (but we include it to show the place exists)
  • 5 in tens place = 50
  • 0 in ones place = 0 (included to complete the pattern)

So: 3,050 = 3,000 + 0 + 50 + 0

However, when simplifying, you can write it as 3,000 + 50 since adding zeros doesn't change the value.

Question: I have trouble remembering when to use hyphens in number names. Is there a pattern?

Answer: Yes! There's a clear pattern for hyphenation in number names:

  • Hyphenate compound numbers from 21-99 except for multiples of 10
  • This includes: twenty-one, thirty-two, forty-three, fifty-four, sixty-five, seventy-six, eighty-seven, ninety-eight
  • Do NOT hyphenate multiples of 10: twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety

Examples:

  • Correct: twenty-one, thirty-five, ninety-nine
  • Incorrect: twenty one, thirty five, ninety nine
  • Correct: twenty, thirty, forty (no hyphens needed)

This pattern helps make number names consistent and easier to read. The hyphen connects the tens and ones digits into a single compound word.