Solved Exercises on Writing Numbers in Different Forms in Grade 4

Master writing numbers in different forms: standard form, expanded form, word form, place value charts, and base ten blocks through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Standard to Expanded Form
Exercise 1
Write 4,567 in expanded form.
Definition:

Expanded form: Shows the value of each digit in a number by breaking it down into its place values.

Method:
  1. Identify the place value of each digit
  2. Write each digit multiplied by its place value
  3. Connect with addition signs
Standard Form
4,567
Expanded Form
4,000 + 500 + 60 + 7
Word Form
Four thousand five hundred sixty-seven
Thousands
Hundreds
Tens
Ones
Decimal
4
5
6
7
0
Step 1: Identify place values

4 is in the thousands place → 4 × 1,000 = 4,000

5 is in the hundreds place → 5 × 100 = 500

6 is in the tens place → 6 × 10 = 60

7 is in the ones place → 7 × 1 = 7

Step 2: Write expanded form

Combine all parts with addition: 4,000 + 500 + 60 + 7

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

4,567 in expanded form is 4,000 + 500 + 60 + 7

Applied rules:

• Place value: Each position has a specific value (ones, tens, hundreds, thousands)

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

• Zero placeholders: Include zeros for empty positions if needed

2 Word to Standard Form
Exercise 2
Write "Three thousand two hundred forty-five" in standard form.
Definition:

Word form: Numbers written out in words using letters.

Standard form: Numbers written using digits (0-9).

Word Form
Three thousand two hundred forty-five
Standard Form
3,245
Expanded Form
3,000 + 200 + 40 + 5
Step 1: Break down the words

"Three thousand" → 3,000

"two hundred" → 200

"forty-five" → 45

Step 2: Combine the parts

3,000 + 200 + 45 = 3,245

Step 3: Write in standard form

Three thousand two hundred forty-five = 3,245

Three thousand two hundred forty-five = 3,245
Final answer:

"Three thousand two hundred forty-five" in standard form is 3,245

Applied rules:

• Word identification: Recognize number words and their place values

• Grouping: Thousands, hundreds, tens, and ones

• Commas: Place commas after every three digits from the right

3 Place Value Chart
Exercise 3
Show 7,824 in a place value chart and write it in expanded form.
Definition:

Place value chart: Organizes digits according to their value (millions, thousands, hundreds, tens, ones).

Ten Thousands
Thousands
Hundreds
Tens
Ones
0
7
8
2
4
cubes
Thousands (7)
flats
Hundreds (8)
rods
Tens (2)
units
Ones (4)
Step 1: Identify place values

7 is in the thousands place → 7 × 1,000 = 7,000

8 is in the hundreds place → 8 × 100 = 800

2 is in the tens place → 2 × 10 = 20

4 is in the ones place → 4 × 1 = 4

Step 2: Write expanded form

7,000 + 800 + 20 + 4

7,824 = 7,000 + 800 + 20 + 4
Final answer:

7,824 in expanded form is 7,000 + 800 + 20 + 4

Applied rules:

• Place value system: Each position is 10 times the value of the position to its right

• Base ten blocks: Visual representation of place values

• Zero placeholders: Use zeros for missing place values

Forms of Numbers, Rules and Methods
Standard: 4,567
Number Forms
Standard Form
4,567
Using digits
Expanded Form
4,000 + 500 + 60 + 7
Value of each digit
Word Form
Four thousand five hundred sixty-seven
Written in words
Key definitions:

Standard form: Numbers written using digits (0-9)

Expanded form: Shows the value of each digit by breaking it into its place values

Word form: Numbers written out in words using letters

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

Complete methodology:
  1. Identify the number: Look at each digit and its position
  2. Understand place values: Ones, tens, hundreds, thousands, etc.
  3. Convert to desired form: Apply conversion rules
  4. Verify your work: Check that all parts add up correctly
Tip 1: Remember the place value order: Ones, Tens, Hundreds, Thousands, Ten Thousands...
Tip 2: In word form, hyphenate compound numbers from twenty-one to ninety-nine.
Tip 3: In expanded form, multiply each digit by its place value.
Tip 4: Always include commas in standard form after every three digits from the right.
Common errors: Forgetting commas, misreading place values, incorrect word spellings.
Memory aids: Think "E for Expanded" means "Each digit gets its own place value".
Essential rules to remember:

• Standard form: Use commas after every three digits from the right

• Expanded form: Each digit × its place value, connected by addition

• Word form: Spell out each group (thousands, hundreds, etc.) separately

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

Solution: Exercises 4 to 5
4 Mixed Forms Practice
Exercise 4
Convert 9,053 to expanded form and word form.
Definition:

Expanded form: Shows the value of each digit by breaking it into its place values.

Word form: Numbers written out in words using letters.

Standard Form
9,053
Expanded Form
9,000 + 0 + 50 + 3
Word Form
Nine thousand fifty-three
Thousands
Hundreds
Tens
Ones
9
0
5
3
Step 1: Identify place values for expanded form

9 is in the thousands place → 9 × 1,000 = 9,000

0 is in the hundreds place → 0 × 100 = 0

5 is in the tens place → 5 × 10 = 50

3 is in the ones place → 3 × 1 = 3

Step 2: Write expanded form

9,000 + 0 + 50 + 3 (can also be written as 9,000 + 50 + 3)

Step 3: Write word form

Nine thousand fifty-three (note: we don't say "zero hundred")

9,053 = 9,000 + 50 + 3 = Nine thousand fifty-three
Final answer:

Expanded form: 9,000 + 50 + 3

Word form: Nine thousand fifty-three

Applied rules:

• Zero handling: In word form, don't say "zero" for empty place values

• Hyphenation: Compound numbers (21-99) use hyphens

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

5 Base Ten Blocks
Exercise 5
Show 6,380 using base ten blocks and write it in all three forms.
Definition:

Base ten blocks: Visual tools representing place values (cubes, flats, rods, units).

cubes
Thousands (6)
flats
Hundreds (3)
rods
Tens (8)
units
Ones (0)
Standard Form
6,380
Expanded Form
6,000 + 300 + 80 + 0
Word Form
Six thousand three hundred eighty
Step 1: Count the base ten blocks

6 thousands cubes → 6,000

3 hundreds flats → 300

8 tens rods → 80

0 ones units → 0

Step 2: Write expanded form

6,000 + 300 + 80 + 0

Step 3: Write word form

Six thousand three hundred eighty (note: no "and zero" at the end)

Step 4: Write standard form

6,380 with comma after thousands

Standard: 6,380
Expanded: 6,000 + 300 + 80 + 0
Word: Six thousand three hundred eighty
Final answer:

Standard form: 6,380

Expanded form: 6,000 + 300 + 80 + 0

Word form: Six thousand three hundred eighty

Applied rules:

• Base ten blocks: Cubes (1,000), Flats (100), Rods (10), Units (1)

• Zero in word form: Don't say "zero" for trailing zeros

• Comma placement: After every three digits from the right

Number Forms Reference Guide
4,567 = 4,000 + 500 + 60 + 7
Number Conversion
Key definitions:

Standard form: Numbers written using digits (0-9) with commas after every three digits from the right

Expanded form: Shows the value of each digit by breaking it into its place values

Word form: Numbers written out in words using letters

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

Complete methodology:
  1. Analyze the number: Identify each digit and its position
  2. Choose the target form: Determine which form to convert to
  3. Apply conversion rules: Follow the appropriate conversion method
  4. Verify your result: Check that all conversions are accurate
Tip 1: Remember the place value sequence: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands...
Tip 2: In word form, use hyphens for compound numbers like twenty-one, thirty-two, etc.
Tip 3: In expanded form, multiply each digit by its place value and connect with addition signs.
Tip 4: Always include commas in standard form after every three digits from the right.
Common errors: Forgetting commas, misreading place values, incorrect word spellings, omitting zeros in expanded form.
Memory aids: Think "E for Expanded" means "Each digit gets its own place value".
Essential formulas and rules:

• Standard form: Use commas after every three digits from the right

• Expanded form: Each digit × its place value, connected by addition

• Word form: Spell out each group (thousands, hundreds, etc.) separately

• Place values: Ones (1), Tens (10), Hundreds (100), Thousands (1,000), Ten Thousands (10,000)

• Zero handling: Don't say "zero" in word form for empty place values

Questions & Answers

Question: I don't understand why we need to learn different ways to write the same number. Why can't we just use standard form all the time?

Answer: Great question! Different forms help us understand numbers better:

  • Expanded form shows the value of each digit - it helps you understand that 4,567 is really 4,000 + 500 + 60 + 7
  • Word form is important for reading and writing numbers in everyday life
  • Standard form is the most efficient way to write numbers

Think of it like having different ways to describe yourself - you might say "I am 9 years old" (standard), "I am nine years old" (word form), or "I am eight years and twelve months old" (expanded form). Each gives different insights!

These different forms also prepare you for more advanced math like addition, subtraction, and understanding decimals.

Question: When I write numbers in word form, I get confused about where to put commas and hyphens. Can you explain the rules?

Answer: Here are the rules for word form:

  • Hyphens: Use hyphens for compound numbers from twenty-one to ninety-nine (twenty-one, thirty-five, forty-eight, etc.)
  • Commas: Don't use commas in word form - instead, separate groups with spaces: "four thousand five hundred sixty-seven"
  • And: Don't use "and" unless you're talking about decimals (which you'll learn later)

Examples:

  • 2,345 = Two thousand three hundred forty-five
  • 1,056 = One thousand fifty-six
  • 789 = Seven hundred eighty-nine

Notice that we don't say "two thousand, three hundred, forty-five" with commas in the words.

Question: What happens when there's a zero in the middle of a number? How do I handle that in expanded form and word form?

Answer: Zeros require special attention:

  • Expanded form: Include the zero's place value. For 4,056: 4,000 + 0 + 50 + 6 (or just 4,000 + 50 + 6)
  • Word form: Skip the zero place entirely. For 4,056: "Four thousand fifty-six" (not "four thousand zero fifty-six")
  • Standard form: Keep the zero: 4,056

More examples:

  • 3,040 = 3,000 + 0 + 40 + 0 = "Three thousand forty"
  • 5,007 = 5,000 + 0 + 0 + 7 = "Five thousand seven"
  • 8,709 = 8,000 + 700 + 0 + 9 = "Eight thousand seven hundred nine"

The zero still holds the place in standard form, but we don't say it in word form.