Understanding Three Digit Numbers Worksheet for 3rd Grade Students

Master three digit numbers through 5 comprehensive exercises with detailed solutions, visual aids, and step-by-step guidance.

Solution: Exercises 1 to 3
1 Place Value Identification
Exercise 1
Identify the place value of each digit in 473
Definition:

Three Digit Number: A number with three digits, representing hundreds, tens, and ones

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 (right to left)
  2. Assign place values: ones, tens, hundreds
  3. Calculate the value of each digit
  4. Express the number as a sum of place values
Step 1: Identify positions

473: 4 is in the hundreds place, 7 is in the tens place, 3 is in the ones place

Step 2: Determine place values

4 hundreds = 400

7 tens = 70

3 ones = 3

Step 3: Express as sum

473 = 400 + 70 + 3

H
T
O
4
7
3
400
70
3
473 = 4 hundreds + 7 tens + 3 ones = 400 + 70 + 3
Final answer:

In 473: 4 represents 400 (hundreds), 7 represents 70 (tens), 3 represents 3 (ones)

Applied rules:

• Place Value Position: Rightmost digit is ones, next is tens, then hundreds

• Value Calculation: Multiply digit by its place value (1, 10, 100)

• Number Composition: A three-digit number is the sum of its place values

2 Expanded Form
Exercise 2
Write 628 in expanded form
Definition:

Expanded Form: Writing a number to show the value of each digit

Place Value Expression: Showing how each digit contributes to the total value

Expanded Form Method:
  1. Identify each digit and its position
  2. Determine the place value of each digit
  3. Express each digit as its value (digit × place value)
  4. Connect with addition signs
Step 1: Identify digits and positions

628: 6 is in hundreds place, 2 is in tens place, 8 is in ones place

Step 2: Calculate place values

6 hundreds = 6 × 100 = 600

2 tens = 2 × 10 = 20

8 ones = 8 × 1 = 8

Step 3: Write in expanded form

628 = 600 + 20 + 8

H
T
O
6
2
8
600
20
8
628 = 600 + 20 + 8
Final answer:

628 in expanded form is 600 + 20 + 8

Applied rules:

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

• Sum Expression: Expanded form shows the sum of place values

• Digit Position: Position determines the multiplier (1, 10, 100)

3 Number Comparison
Exercise 3
Compare 357 and 375 using place value
Definition:

Number Comparison: Determining which number is greater, lesser, or equal

Place Value Comparison: Comparing numbers by examining each place value from left to right

Number Comparison Method:
  1. Compare digits in the highest place value first
  2. If digits are equal, move to the next lower place value
  3. Continue until a difference is found
  4. Determine which number is greater based on the comparison
Step 1: Compare hundreds place

357: 3 hundreds, 375: 3 hundreds

Both have 3 hundreds, so move to tens place

Step 2: Compare tens place

357: 5 tens, 375: 7 tens

5 < 7, so 357 < 375

Step 3: Verify with expanded forms

357 = 300 + 50 + 7 = 357

375 = 300 + 70 + 5 = 375

Since 357 < 375, the comparison is correct

H
T
O
3
5
7
3
7
5
vs
vs
vs
357 < 375
Final answer:

357 is less than 375 because 5 tens < 7 tens (when hundreds are equal)

Applied rules:

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

• Place Value Hierarchy: Higher place values determine the comparison

• Sequential Evaluation: Move to lower places only when upper places are equal

Three Digit Number Concepts
473 = 4×100 + 7×10 + 3×1
Three Digit Number Structure
Place Value
H T O
Hundreds, Tens, Ones
Range
100-999
Three digit numbers
Expanded Form
400+70+3
For 473
Key definitions:

Three Digit Number: A number with exactly three digits (from 100 to 999)

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

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

Three Digit Number Analysis:
  1. Digit Identification: Recognize each digit's position
  2. Place Value Assignment: Assign hundreds, tens, or ones
  3. Value Calculation: Multiply digit by its place value
  4. Number Composition: Express as sum of place values
  5. Comparison: Compare using place value hierarchy
Tip 1: Always read three-digit numbers from left to right (hundreds, tens, ones).
Tip 2: The hundreds place is worth 100 times the digit, tens worth 10 times, ones worth 1 time.
Tip 3: When comparing, start with the largest place value first.
Tip 4: Expanded form shows exactly how each digit contributes to the total value.
Solution: Exercises 4 to 5
4 Number Patterns
Exercise 4
What number comes next in this pattern: 234, 244, 254, 264, ___?
Definition:

Number Pattern: A sequence of numbers following a specific rule

Place Value Pattern: A pattern based on changes in specific place values

Step 1: Analyze the pattern

234 → 244 → 254 → 264

Looking at place values:

234: 200 + 30 + 4

244: 200 + 40 + 4

254: 200 + 50 + 4

264: 200 + 60 + 4

Step 2: Identify the rule

Hundreds place: stays at 2

Tens place: increases by 1 each time (3→4→5→6)

Ones place: stays at 4

Rule: Increase the tens place by 1 each time

Step 3: Apply the rule

Next number: 200 + 70 + 4 = 274

Step 4: Verify the pattern

234 → 244 (+10) → 254 (+10) → 264 (+10) → 274 (+10)

Each number increases by 10

The next number is 274
Final answer:

The next number in the pattern is 274

Applied rules:

• Pattern Recognition: Examine each place value separately

• Sequential Analysis: Look for consistent changes

• Place Value Focus: Identify which place(s) are changing

5 Word Problem with Three Digit Numbers
Exercise 5
Sarah collected 428 seashells. Her friend collected 375 seashells. Who collected more? How many more?
Definition:

Word Problems: Real-life scenarios requiring mathematical operations

Comparison Problems: Questions asking to identify greater/lesser quantities

Step 1: Identify the numbers to compare

Sarah: 428 seashells

Friend: 375 seashells

Step 2: Compare using place value

428 vs 375

Hundreds: 4 > 3, so 428 > 375

Sarah collected more seashells

Step 3: Calculate the difference

428 - 375 = ?

Using place value: (400-300) + (20-70) + (8-5)

Need to borrow: 428 = 300 + 120 + 8 = 300 + 110 + 18

Then: (300-300) + (110-70) + (18-5) = 0 + 40 + 13 = 53

Step 4: State the complete answer

Sarah collected more seashells (428 > 375)

Sarah collected 53 more seashells than her friend

H
T
O
4
2
8
3
7
5
Sarah collected more seashells (428 > 375), 53 more than her friend
Final answer:

Sarah collected more seashells. She collected 53 more than her friend.

Applied rules:

• Problem Analysis: Identify numbers and what's being asked

• Place Value Comparison: Use place value to determine greater number

• Subtraction Application: Calculate the difference between numbers

Complete Summary: Understanding Three Digit Numbers
473 = 400 + 70 + 3 = 4×100 + 7×10 + 3×1
Three Digit Number Representation
Key definitions:

Three Digit Number: A number with exactly three digits ranging from 100 to 999

Place Value: Each digit has a value based on its position (hundreds, tens, ones)

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

Complete methodology:
  1. Digit Recognition: Identify each digit in the number
  2. Position Assignment: Assign hundreds, tens, or ones position
  3. Value Calculation: Multiply each digit by its place value (100, 10, 1)
  4. Number Expression: Write as sum of place values
  5. Comparison: Compare using place value hierarchy
  6. Application: Use in word problems and patterns
Tip 1: The leftmost digit represents hundreds (multiply by 100).
Tip 2: The middle digit represents tens (multiply by 10).
Tip 3: The rightmost digit represents ones (multiply by 1).
Tip 4: When comparing, start with the largest place value first.
Common errors: Confusing place values, forgetting to multiply by place value, starting comparisons from the wrong direction.
Key concepts: Each place is 10 times the value of the place to its right.
Three Digit Number Rules:

• Position Value: Hundreds place = digit × 100, Tens place = digit × 10, Ones place = digit × 1

• Range: Three digit numbers range from 100 to 999

• Comparison: Compare from left to right (highest place value first)

• Expanded Form: Write as sum of each digit's place value

• Base Ten System: Each place is 10 times the value of the place to its right

Three Digit Number Visualization Exercise
Exercise 6: Visual Number Representation
Represent 542 using base ten blocks and expanded form

Visualization: Understanding three digit numbers through concrete representations.

5 hundreds
4 tens
2 ones
= 500
= 40
= 2
Expanded:
500 + 40 + 2
= 542

Analysis: 542 consists of 5 groups of 100, 4 groups of 10, and 2 individual units.

Result: 542 = 500 + 40 + 2

Questions & Answers

Question: My child struggles with understanding that the same digit has different values depending on its position. How can I help?

Answer: This is a common challenge! Try these concrete approaches:

  • Base Ten Blocks: Use physical blocks to show 1 hundred block vs 1 ten rod vs 1 unit cube
  • Money Connection: Relate to dollars ($100), dimes ($10), and pennies ($1)
  • Place Value Charts: Write numbers in columns to visually separate positions
  • Verbal Reinforcement: Say "four hundreds" not just "four" when reading 473

The key is connecting the abstract symbol to its concrete value through multiple representations.

Question: Why do we need to learn expanded form? It seems like extra work.

Answer: Expanded form is actually very helpful because it:

  • Builds Understanding: Shows exactly how each digit contributes to the total
  • Prevents Errors: Helps avoid mistakes in addition and subtraction
  • Prepares for Advanced Math: Essential for understanding decimals and larger numbers
  • Improves Mental Math: Makes it easier to add and subtract mentally
  • Shows Number Relationships: Reveals the structure of our number system

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

Question: When comparing numbers, why do we start from the left side instead of the right?

Answer: We start from the left because the leftmost digits have the greatest value:

  • Highest Impact: The hundreds place is worth much more than tens or ones
  • Efficiency: Often we can decide which number is bigger by just looking at the first digit
  • Logical Order: It's like comparing the biggest parts first, then the smaller parts
  • Consistency: This method works for any number of digits

For example, 300 is much bigger than 299, even though 299 has larger digits in the tens and ones places.