Solved Exercises on Place Value to Thousands in Grade 3

Master place value to thousands: understanding thousands, hundreds, tens, and ones through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Identifying Place Values
Exercise 1
In the number 4,729, what is the value of each digit?
Definition:

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

Place Value Identification Method:
  1. Identify the position of each digit
  2. Match the position to its place value name
  3. Calculate the value of each digit
  4. Express the total value
Thousands
4
4 × 1,000 = 4,000
Hundreds
7
7 × 100 = 700
Tens
2
2 × 10 = 20
Ones
9
9 × 1 = 9
Step 1: Identify the thousands digit

In 4,729, the digit in the thousands place is 4

Value: 4 × 1,000 = 4,000

Step 2: Identify the hundreds digit

In 4,729, the digit in the hundreds place is 7

Value: 7 × 100 = 700

Step 3: Identify the tens digit

In 4,729, the digit in the tens place is 2

Value: 2 × 10 = 20

Step 4: Identify the ones digit

In 4,729, the digit in the ones place is 9

Value: 9 × 1 = 9

4,729 = 4,000 + 700 + 20 + 9
Four thousand seven hundred twenty-nine
Final answer:

4 = 4,000, 7 = 700, 2 = 20, 9 = 9

Applied rules:

• Position Value: Each position represents a power of 10

• Thousand Place: 1,000 × digit value

• Expanded Form: Add the value of each digit

2 Writing Expanded Form
Exercise 2
Write 6,384 in expanded form.
Definition:

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

Thousands
6
6 × 1,000 = 6,000
Hundreds
3
3 × 100 = 300
Tens
8
8 × 10 = 80
Ones
4
4 × 1 = 4
Step 1: Identify each digit's place value

6 is in thousands place = 6,000

3 is in hundreds place = 300

8 is in tens place = 80

4 is in ones place = 4

Step 2: Write as addition

6,000 + 300 + 80 + 4

Step 3: Verify the sum

6,000 + 300 + 80 + 4 = 6,384 ✓

6,384 = 6,000 + 300 + 80 + 4
Six thousand three hundred eighty-four
Final answer:

6,000 + 300 + 80 + 4

Applied rules:

• Place Value Multiplication: Each digit × its place value

• Summation: Add all place values together

• Verification: Check that the sum equals the original number

3 Converting to Word Form
Exercise 3
Write 8,052 in word form.
Definition:

Word Form: Writing a number using words instead of digits.

Thousands
8
Eight thousand
Hundreds
0
(no hundreds)
Tens
5
fifty
Ones
2
two
Step 1: Identify thousands

8 in thousands place = eight thousand

Step 2: Handle hundreds place

0 in hundreds place = no hundreds (skip this part)

Step 3: Identify tens and ones

5 in tens place and 2 in ones place = fifty-two

Step 4: Combine all parts

Eight thousand fifty-two

8,052 = 8,000 + 0 + 50 + 2
Eight thousand fifty-two
Final answer:

Eight thousand fifty-two

Applied rules:

• Zero Handling: Skip zeros in hundreds or tens places

• Compound Numbers: Use hyphens for 21-99 (twenty-one, thirty-five)

• Thousand Grouping: Say thousands part first, then the rest

Place Value Systems and Concepts
Digit × Place Value = Actual Value
Place Value Formula
Place Values
Thousands, Hundreds, Tens, Ones
Position system
Value System
1000s, 100s, 10s, 1s
Power of 10
Forms
Standard, Expanded, Word
Number representations
Key Definitions:

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

Thousands Place: The fourth digit from the right, representing 1,000s

Hundreds Place: The third digit from the right, representing 100s

Tens Place: The second digit from the right, representing 10s

Ones Place: The first digit from the right, representing 1s

Standard Form: Writing numbers using digits (e.g., 4,729)

Expanded Form: Writing numbers as the sum of each place value (e.g., 4,000 + 700 + 20 + 9)

Word Form: Writing numbers using words (e.g., four thousand seven hundred twenty-nine)

Complete Place Value Method:
  1. Position Identification: Find the position of each digit
  2. Value Assignment: Assign the correct place value to each digit
  3. Calculation: Multiply each digit by its place value
  4. Conversion: Change between different number forms
  5. Verification: Check that all forms represent the same number
Tip 1: Remember the order: Thousands, Hundreds, Tens, Ones (THOUSAND).
Tip 2: Use commas to separate thousands from hundreds (e.g., 5,803).
Tip 3: Zeros hold place values but have no value themselves.
Tip 4: Practice with base-ten blocks to visualize place values.
Tip 5: Always verify your expanded form equals the original number.
Place Values: Thousands (1,000), Hundreds (100), Tens (10), Ones (1).
Number Forms: Standard (digits), Expanded (addition), Word (spelled out).
Essential Place Value Rules:

• Position Matters: Each position has a specific value (1,000s, 100s, 10s, 1s)

• Multiplication Rule: Digit × Place Value = Actual Value

• Zero Rule: Zeros hold place values but contribute no value

• Consistency Rule: All forms must represent the same number

• Verification Rule: Always check your work

Solution: Exercises 4 to 5
4 Building Numbers
Exercise 4
What number has 7 thousands, 0 hundreds, 3 tens, and 9 ones?
Definition:

Number Construction: Building a number from its place value components.

Step 1: Identify each component

7 thousands = 7,000

0 hundreds = 0

3 tens = 30

9 ones = 9

Step 2: Write each place value

Thousands: 7

Hundreds: 0

Tens: 3

Ones: 9

Step 3: Combine to form the number

7,039

Step 4: Verify the expanded form

7,000 + 0 + 30 + 9 = 7,039 ✓

Thousands
7
Hundreds
0
Tens
3
Ones
9
7,039 = 7,000 + 0 + 30 + 9
Seven thousand thirty-nine
Final answer:

The number is 7,039.

Applied rules:

• Component Assembly: Put together each place value component

• Zero Handling: Include zeros in their correct positions

• Verification: Check that the constructed number matches all components

5 Place Value Relationships
Exercise 5
In the number 9,406, how many times greater is the 9 than the 6?
Definition:

Place Value Relationships: Comparing the actual values of different digits in a number.

Step 1: Identify the place value of each digit

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

6 is in ones place = 6 × 1 = 6

Step 2: Set up the relationship

How many times greater is 9,000 than 6?

Step 3: Calculate the relationship

9,000 ÷ 6 = 1,500

Step 4: Interpret the result

The 9 in the thousands place is 1,500 times greater than the 6 in the ones place

Thousands
9,000
Hundreds
0
Tens
0
Ones
6
9,000
÷
6
=
1,500
Final answer:

The 9 is 1,500 times greater than the 6.

Applied rules:

• Actual Value: Compare the actual values, not just the digits

• Division: Use division to find "how many times greater"

• Place Value Impact: Understand how position affects value

Complete Guide to Place Value to Thousands
Number = (Thousands × 1,000) + (Hundreds × 100) + (Tens × 10) + (Ones × 1)
Place Value Formula
Key definitions:

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

Digit: Any of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9

Number: A mathematical object used to count, measure, and label

Standard Form: Writing numbers using digits (e.g., 4,729)

Expanded Form: Writing numbers as the sum of each place value (e.g., 4,000 + 700 + 20 + 9)

Word Form: Writing numbers using words (e.g., four thousand seven hundred twenty-nine)

Base-10 System: Our number system based on powers of 10

Position: The location of a digit in a number

Complete Place Value Analysis Method:
  1. Digit Identification: Locate each digit in the number
  2. Position Determination: Identify the place value of each digit
  3. Value Calculation: Multiply each digit by its place value
  4. Form Conversion: Change between standard, expanded, and word forms
  5. Relationship Analysis: Compare place values within the number
  6. Verification: Check that all forms represent the same value
Tip 1: Use place value charts to organize digits and their values.
Tip 2: Remember that each position is 10 times the previous position.
Tip 3: Zeros hold place values but contribute no numerical value.
Tip 4: Practice converting between all three number forms regularly.
Tip 5: Use base-ten blocks to visualize place value relationships.
Place Value Hierarchy: Thousands (1,000), Hundreds (100), Tens (10), Ones (1).
Number Forms: Standard (digits), Expanded (addition), Word (written).
Common Challenges: Zero placement, digit value confusion, form conversion errors.
Fundamental Place Value Rules:

• Position Value: Each position represents a power of 10

• Base-10 Multiplication: Each position is 10 times the previous

• Zero Holding: Zeros maintain position but add no value

• Form Consistency: All forms represent the same numerical value

• Verification Rule: Always check that conversions are accurate

Real World Applications: Money amounts, population counts, distances, measurements, inventory.
Future Connections: Paves the way for larger numbers, decimals, and advanced place value concepts.

Questions & Answers

Question: My child confuses the value of digits in different places. How can I help them understand that 5 in the thousands place is different from 5 in the ones place?

Answer: Here are effective strategies to clarify digit values:

  • Use base-ten blocks: Show that 5 thousands blocks are much larger than 5 unit blocks
  • Money analogy: Compare to $5,000 vs $5
  • Place value charts: Visually organize digits with their values
  • Expanded form: Write 5,000 = 5 × 1,000 and 5 = 5 × 1

Practice with real examples: "Would you rather have 5 dollars or 5 thousand dollars?" This helps them understand the magnitude difference.

Emphasize that the position of the digit determines its value, not just the digit itself.

Question: Why do we need to learn place value? It seems hard.

Answer: Place value is super important! Here's why:

  • Reading big numbers: Helps you read numbers like 10,000 or 5,678
  • Math operations: Makes addition, subtraction, multiplication, and division easier
  • Real life: Helps with money, age, scores, addresses
  • Understanding: Knows what each number really means

Think of place value like a secret code that helps you understand all numbers! Once you know it, big numbers become easier.

Practice with fun examples like your age, house number, or how many books you own!

Question: How can I help students who struggle with zeros in the middle of numbers when writing word form?

Answer: Here are strategies for handling zeros in word form:

  1. Zero in hundreds place: Skip entirely (4,052 = "four thousand fifty-two")
  2. Zero in tens place: Still connect to ones (4,502 = "four thousand five hundred two")
  3. Visual charts: Show which places to skip and which to include
  4. Practice patterns: Start with simple examples and build complexity
  5. Sentence frames: "___ thousand ___ hundred ___"

Create anchor charts showing examples: 4,052, 4,502, 4,002 to highlight the differences.

Emphasize that zeros hold place value but don't get pronounced in word form.