Solved Exercises on Number Form Questions in Grade 4

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

Solution: Exercises 1 to 3
1 Standard form to expanded and word form question
Exercise 1
Write the number 7,842 in expanded form and word form.
Definition:

Standard form: The regular way we write numbers (e.g., 7,842)

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

Word form: Writing numbers using words (e.g., seven thousand eight hundred forty-two)

Conversion Method:
  1. Identify the place value of each digit
  2. Write each digit multiplied by its place value for expanded form
  3. Combine the parts with addition signs
  4. Write the number using words for word form
Standard Form
7,842
Expanded Form
7,000 + 800 + 40 + 2
Word Form
Seven thousand eight hundred forty-two
Step 1: Identify place values

7 is in thousands place: 7 × 1,000 = 7,000

8 is in hundreds place: 8 × 100 = 800

4 is in tens place: 4 × 10 = 40

2 is in ones place: 2 × 1 = 2

Step 2: Write in expanded form

7,842 = 7,000 + 800 + 40 + 2

Step 3: Write in word form

7,842 = Seven thousand eight hundred forty-two

Step 4: Verify the calculation

7,000 + 800 + 40 + 2 = 7,842 ✓

Standard Form: 7,842
Expanded Form: 7,000 + 800 + 40 + 2
Word Form: Seven thousand eight hundred forty-two
Final answer:

Expanded Form: 7,000 + 800 + 40 + 2

Word Form: Seven thousand eight hundred forty-two

Applied rules:

• Place Value Multiplication: Each digit multiplied by its place value

• Expanded Form Format: Sum of place values

• Word Form: Read number aloud and write the words

• Verification: Sum of parts equals original number

2 Number form questions with zeros
Exercise 2
Write 9,063 in standard form, expanded form, and word form.
Definition:

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

Standard Form
9,063
Expanded Form
9,000 + 0 + 60 + 3
Simplified
9,000 + 60 + 3
Word Form
Nine thousand sixty-three
Step 1: Identify place values

9 is in thousands place: 9 × 1,000 = 9,000

0 is in hundreds place: 0 × 100 = 0

6 is in tens place: 6 × 10 = 60

3 is in ones place: 3 × 1 = 3

Step 2: Write in expanded form

9,063 = 9,000 + 0 + 60 + 3

Step 3: Simplify by omitting zero terms

9,063 = 9,000 + 60 + 3

Step 4: Write in word form

9,063 = Nine thousand sixty-three

Step 5: Verify the calculation

9,000 + 60 + 3 = 9,063 ✓

Standard Form: 9,063
Expanded Form: 9,000 + 60 + 3
Word Form: Nine thousand sixty-three
Final answer:

Expanded Form: 9,000 + 60 + 3

Word Form: Nine thousand sixty-three

Applied rules:

• Zero Inclusion: Zeros are written as their place value

• Simplification: Terms with 0 can be omitted

• Word Form: Skip "and" when reading numbers

• Verification: Sum of parts equals original number

3 Converting expanded form to standard and word form question
Exercise 3
What number is represented by 50,000 + 7,000 + 0 + 80 + 4? Write it in standard form and word form.
Definition:

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

Expanded Form
50,000 + 7,000 + 0 + 80 + 4
Standard Form
57,084
Word Form
Fifty-seven thousand eighty-four
Step 1: Add all parts of the expanded form

50,000 + 7,000 + 0 + 80 + 4 = 57,084

Step 2: Write in standard form

57,084

Step 3: Write in word form

57,084 = Fifty-seven thousand eighty-four

Step 4: Verify by converting back to expanded form

57,084 = 50,000 + 7,000 + 0 + 80 + 4 ✓

Expanded Form: 50,000 + 7,000 + 0 + 80 + 4
Standard Form: 57,084
Word Form: Fifty-seven thousand eighty-four
Final answer:

Standard Form: 57,084

Word Form: Fifty-seven thousand eighty-four

Applied rules:

• Place Value Addition: Sum all expanded form parts

• Digit Placement: Each part corresponds to a specific place

• Word Form: Read number aloud and write the words

• Verification: Convert back to ensure accuracy

Number Form Questions Rules
\(7,842 = 7,000 + 800 + 40 + 2\)
Number Form Questions 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., 7,842)

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

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

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

Number Sense: Understanding the relationships between numbers and their values

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. Convert to words: Read the number aloud and write the words
  5. 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 number forms.
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

• Number Forms: Standard, Expanded, Word

Solution: Exercises 4 to 5
4 Mixed number form questions
Exercise 4
Complete the table for the number 8,307:
Form Representation
Standard Form _______
Expanded Form _______
Word Form _______
Definition:

Number form questions: Working with all three forms of a number simultaneously

Standard Form
8,307
Expanded Form
8,000 + 300 + 0 + 7
Word Form
Eight thousand three hundred seven
Step 1: Identify place values for expanded form

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

3 is in hundreds place: 3 × 100 = 300

0 is in tens place: 0 × 10 = 0

7 is in ones place: 7 × 1 = 7

Step 2: Write in expanded form

8,307 = 8,000 + 300 + 0 + 7

Step 3: Write in word form

8,307 = Eight thousand three hundred seven

Step 4: Verify all forms are equivalent

8,000 + 300 + 0 + 7 = 8,307 ✓

Standard Form: 8,307
Expanded Form: 8,000 + 300 + 7
Word Form: Eight thousand three hundred seven
Final answer:
Form Representation
Standard Form 8,307
Expanded Form 8,000 + 300 + 7
Word Form Eight thousand three hundred seven
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 Number form matching question
Exercise 5
Match the number forms below:
  • Standard Form: 46,058
  • Expanded Form: _______
  • Word Form: _______
Definition:

Number form matching: Converting between different representations of the same number

Standard Form
46,058
Expanded Form
40,000 + 6,000 + 0 + 50 + 8
Word Form
Forty-six thousand fifty-eight
Step 1: Identify place values for expanded form

4 is in ten-thousands place: 4 × 10,000 = 40,000

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

0 is in hundreds place: 0 × 100 = 0

5 is in tens place: 5 × 10 = 50

8 is in ones place: 8 × 1 = 8

Step 2: Write in expanded form

46,058 = 40,000 + 6,000 + 0 + 50 + 8

Step 3: Write in word form

46,058 = Forty-six thousand fifty-eight

Step 4: Verify by converting back to standard form

40,000 + 6,000 + 0 + 50 + 8 = 46,058 ✓

Standard Form: 46,058
Expanded Form: 40,000 + 6,000 + 50 + 8
Word Form: Forty-six thousand fifty-eight
Final answer:
  • Standard Form: 46,058
  • Expanded Form: 40,000 + 6,000 + 50 + 8
  • Word Form: Forty-six thousand fifty-eight
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 Questions
\(d_n \times 10^n + d_{n-1} \times 10^{n-1} + ... + d_1 \times 10^1 + d_0 \times 10^0\)
General Expanded Form Formula
Key definitions:

Standard Form: The usual way we write numbers (e.g., 7,842)

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

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

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

Number Sense: Understanding the relationships between numbers and their values

Number Form Questions: Problems that require converting between different number forms

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. Word formation: Read the number aloud and write the words
  5. 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 Questions Visualization: Different Representations
Exercise 6: Understanding Number Forms
Consider the following number and its different forms:
Standard: 5,678
Expanded: 5,000 + 600 + 70 + 8
Word: Five thousand six hundred seventy-eight

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

  • Standard Form: 5,678 (Five thousand six hundred seventy-eight)
  • Expanded Form: 5,000 + 600 + 70 + 8 (Five thousands + Six hundreds + Seven tens + Eight ones)
  • Word Form: Five thousand six hundred seventy-eight

Questions & Answers

Question: I don't understand why we need to answer number form questions. Why can't we just write numbers normally?

Answer: Great question! Number form questions are crucial for understanding how our number system works:

  • They help you understand what each digit means in a number
  • They build a foundation for addition and subtraction with regrouping
  • They prepare you for working with larger numbers and decimals later
  • They make it easier to compare numbers and understand their magnitude
  • They show the relationship between digits and their place values
  • They help with reading and writing numbers in different contexts

For example, in expanded form (7,000 + 800 + 40 + 2), you can see that the 7 represents 7 thousands (7,000), not just 7. This helps you understand the true value of each digit!

Question: My child gets confused when there are zeros in the expanded form like 9,063 = 9,000 + 0 + 60 + 3. How do I explain this?

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

  • In 9,063 = 9,000 + 0 + 60 + 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 9,063: 9 thousands, 0 hundreds, 6 tens, 3 ones
  • The zero keeps the 6 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 9,000 + 60 + 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., 7,842)
  • Expanded Form: Shows each digit's place value (e.g., 7,000 + 800 + 40 + 2)
  • Word Form: Shows the number written out in words (e.g., seven thousand eight hundred forty-two)
  • Converting Standard to Expanded: Break apart each digit by its place value
  • Converting Expanded to Standard: Add all the parts together

Standard Form: 7,842

Expanded Form: 7,000 + 800 + 40 + 2

Word Form: Seven thousand eight hundred forty-two

To convert from expanded to standard: 7,000 + 800 + 40 + 2 = 7,842

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