Expanded Form Questions for Class 3 - Place Value Mastery with Hundreds

Complete collection of expanded form questions with detailed solutions, comprehensive summary, and visual aids for place value understanding including hundreds.

Solution: Exercises 1 to 3
1 Basic hundreds, tens and ones
Exercise 1
Write 247 in expanded form.
Show how many hundreds, tens and ones are in 247.
Definition:

Expanded form: Writing a number as the sum of its place values. For 3-digit numbers: hundreds + tens + ones

Method for expanded form:
  1. Identify the digit in the hundreds place
  2. Identify the digit in the tens place
  3. Identify the digit in the ones place
  4. Write the hundreds value as (digit × 100)
  5. Write the tens value as (digit × 10)
  6. Write the ones value as (digit × 1)
  7. Add them together
2
HUNDREDS PLACE
→
200
2 × 100
4
TENS PLACE
→
40
4 × 10
7
ONES PLACE
→
7
7 × 1
HUNDREDS
2
TENS
4
ONES
7
Step 1: Identify place values

In 247: HUNDREDS = 2, TENS = 4, ONES = 7

Step 2: Calculate each place value

2 hundreds = 2 × 100 = 200

4 tens = 4 × 10 = 40

7 ones = 7 × 1 = 7

Step 3: Write in expanded form

247 = 200 + 40 + 7

247 = 200 + 40 + 7
Final answer:

247 in expanded form is 200 + 40 + 7

247 has 2 hundreds, 4 tens and 7 ones

Applied rules:

• Place value rule: Each digit's value depends on its position

• Expanded form rule: Add the values of each place

• Hundreds rule: Hundreds digit × 100 gives the hundreds value

• Tens rule: Tens digit × 10 gives the tens value

• Ones rule: Ones digit × 1 gives the ones value

2 Decomposition practice
Exercise 2
Write 385 in expanded form.
Break down 385 into hundreds, tens and ones.
Definition:

Number decomposition: Breaking a number into its component parts based on place value

3
HUNDREDS PLACE
→
300
3 × 100
8
TENS PLACE
→
80
8 × 10
5
ONES PLACE
→
5
5 × 1
HUNDREDS
3
TENS
8
ONES
5
Step 1: Identify place values

In 385: HUNDREDS = 3, TENS = 8, ONES = 5

Step 2: Calculate each place value

3 hundreds = 3 × 100 = 300

8 tens = 8 × 10 = 80

5 ones = 5 × 1 = 5

Step 3: Write in expanded form

385 = 300 + 80 + 5

385 = 300 + 80 + 5
Final answer:

385 in expanded form is 300 + 80 + 5

385 has 3 hundreds, 8 tens and 5 ones

Applied rules:

• Place value identification: Leftmost digit is hundreds, middle is tens, rightmost is ones

• Value calculation: Hundreds × 100, Tens × 10, Ones × 1

• Addition principle: Combine place values with addition

3 Understanding place value
Exercise 3
Write 562 in expanded form.
Show the relationship between digits and their values.
Definition:

Place value relationship: The position of a digit determines its actual value in the number

5
HUNDREDS PLACE
→
500
5 × 100
6
TENS PLACE
→
60
6 × 10
2
ONES PLACE
→
2
2 × 1
HUNDREDS
5
TENS
6
ONES
2
Step 1: Identify place values

In 562: HUNDREDS = 5, TENS = 6, ONES = 2

Step 2: Calculate each place value

5 hundreds = 5 × 100 = 500

6 tens = 6 × 10 = 60

2 ones = 2 × 1 = 2

Step 3: Write in expanded form

562 = 500 + 60 + 2

562 = 500 + 60 + 2
Final answer:

562 in expanded form is 500 + 60 + 2

562 has 5 hundreds, 6 tens and 2 ones

Applied rules:

• Position matters: Hundreds place is worth 100 times the digit

• Tens place: Worth 10 times the digit

• Ones place: Digit value equals itself

• Summation: Total value is the sum of all place values

Place Value Rules and Methods
3-digit number = (hundreds digit × 100) + (tens digit × 10) + (ones digit × 1)
Expanded Form Formula
Hundreds Rule
Hundreds × 100
Leftmost digit value
Tens Rule
Tens × 10
Middle digit value
Ones Rule
Ones × 1
Rightmost digit value
Key definitions:

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

Expanded form: Writing a number as the sum of its place values

Hundreds: The leftmost digit in a 3-digit number, worth 100 times its face value

Tens: The middle digit in a 3-digit number, worth 10 times its face value

Ones: The rightmost digit in a 3-digit number, worth its face value

Complete methodology:
  1. Identify positions: Recognize hundreds, tens and ones places
  2. Extract digits: Separate the hundreds, tens and ones digits
  3. Calculate values: Multiply hundreds by 100, tens by 10, ones by 1
  4. Write expanded form: Express as sum of place values
Tip 1: Remember: hundreds place is worth 100 times the digit.
Tip 2: Always write expanded form with addition signs (+).
Tip 3: Check your work by adding the expanded parts to get the original number.
Common errors: Forgetting to multiply hundreds by 100, confusing digit positions.
Key concept: In expanded form, we show the actual value each digit contributes to the total number.
Place Value Rules:

• Left digit: Always represents hundreds in 3-digit numbers

• Middle digit: Always represents tens in 3-digit numbers

• Right digit: Always represents ones in 3-digit numbers

• Value calculation: Hundreds digit × 100, Tens digit × 10, Ones digit × 1

• Expanded form: Sum of calculated place values

• Verification: Adding expanded parts should equal original number

253
200 + 50 + 3
476
400 + 70 + 6
839
800 + 30 + 9
164
100 + 60 + 4
Solution: Exercises 4 to 5
4 Advanced place value
Exercise 4
Write 691 in expanded form.
Show how 691 is composed of hundreds, tens and ones.
Definition:

Number composition: Understanding how digits combine to form a whole number

6
HUNDREDS PLACE
→
600
6 × 100
9
TENS PLACE
→
90
9 × 10
1
ONES PLACE
→
1
1 × 1
HUNDREDS
6
TENS
9
ONES
1
Step 1: Identify place values

In 691: HUNDREDS = 6, TENS = 9, ONES = 1

Step 2: Calculate each place value

6 hundreds = 6 × 100 = 600

9 tens = 9 × 10 = 90

1 ones = 1 × 1 = 1

Step 3: Write in expanded form

691 = 600 + 90 + 1

691 = 600 + 90 + 1
Final answer:

691 in expanded form is 600 + 90 + 1

691 has 6 hundreds, 9 tens and 1 ones

Applied rules:

• Position identification: Leftmost digit is hundreds place

• Value multiplication: Hundreds digit multiplied by 100

• Summation: Add place values to form expanded notation

5 Comprehensive practice
Exercise 5
Write 748 in expanded form.
Demonstrate complete understanding of place value.
Definition:

Place value mastery: Understanding how each position contributes to the overall number value

7
HUNDREDS PLACE
→
700
7 × 100
4
TENS PLACE
→
40
4 × 10
8
ONES PLACE
→
8
8 × 1
HUNDREDS
7
TENS
4
ONES
8
Step 1: Identify place values

In 748: HUNDREDS = 7, TENS = 4, ONES = 8

Step 2: Calculate each place value

7 hundreds = 7 × 100 = 700

4 tens = 4 × 10 = 40

8 ones = 8 × 1 = 8

Step 3: Write in expanded form

748 = 700 + 40 + 8

748 = 700 + 40 + 8
Final answer:

748 in expanded form is 700 + 40 + 8

748 has 7 hundreds, 4 tens and 8 ones

Applied rules:

• Place value recognition: Systematic identification of digit positions

• Value computation: Proper multiplication of digits by their place value

• Notation: Expressing as sum of individual place values

Comprehensive Summary: Place Value and Expanded Form
Complete Learning Guide

This comprehensive summary covers all aspects of expanded form for class 3 students, providing clear explanations, methods, and examples for mastering place value concepts including hundreds, tens, and ones.

Key Definitions

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

Expanded Form: Writing a number as the sum of its place values (e.g., 247 = 200 + 40 + 7).

Hundreds Place: The leftmost position in a 3-digit number, worth 100 times the digit's face value.

Tens Place: The middle position in a 3-digit number, worth 10 times the digit's face value.

Ones Place: The rightmost position in a 3-digit number, worth the digit's face value.

Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 used to make numbers.

Core Rules and Laws

Position Rule: In a 3-digit number, the left digit is always the hundreds place, the middle is always the tens place, and the right digit is always the ones place.

Value Rule: Hundreds digit × 100 = actual hundreds value; Tens digit × 10 = actual tens value; Ones digit × 1 = actual ones value.

Summation Rule: Expanded form is the sum of all place values.

Verification Rule: Adding expanded parts should equal the original number.

Consistency Rule: The same method works for any 3-digit number.

Step-by-Step Methods

Method 1: Standard Approach

  1. Identify the hundreds digit (leftmost)
  2. Identify the tens digit (middle)
  3. Identify the ones digit (rightmost)
  4. Multiply hundreds digit by 100
  5. Multiply tens digit by 10
  6. Multiply ones digit by 1
  7. Add the results together

Method 2: Verification Approach

  1. Write expanded form
  2. Add the expanded parts
  3. Check if result equals original number
Examples (Simple to Advanced)

Simple Examples:

123 = 100 + 20 + 3 (1 hundred + 2 tens + 3 ones)

234 = 200 + 30 + 4 (2 hundreds + 3 tens + 4 ones)

Intermediate Examples:

456 = 400 + 50 + 6 (4 hundreds + 5 tens + 6 ones)

789 = 700 + 80 + 9 (7 hundreds + 8 tens + 9 ones)

Advanced Examples:

901 = 900 + 0 + 1 (9 hundreds + 0 tens + 1 one)

543 = 500 + 40 + 3 (5 hundreds + 4 tens + 3 ones)

Tips, Tricks, and Pitfalls

Tips:

  • Always multiply hundreds digit by 100
  • Always multiply tens digit by 10
  • Ones digit stays the same
  • Check by adding expanded parts

Common Mistakes:

  • Forgetting to multiply hundreds by 100
  • Confusing hundreds, tens and ones positions
  • Omitting addition signs in expanded form
Key Notes for Memorization

Memory Aids:

  • "Hundreds are huge!" - They multiply by 100
  • "Tens are big!" - They multiply by 10
  • "Ones stay small" - They stay as themselves
  • "Left is hundreds, middle is tens, right is ones"

Quick Check: Always add expanded parts to verify your answer equals the original number.

Pattern Recognition: In expanded form, the first number is always a multiple of 100, the second is always a multiple of 10, the third is always less than 10.

Questions & Answers

Question: I don't understand why 247 becomes 200 + 40 + 7. Why isn't it just 2 + 4 + 7?

Answer: Great question! The key is understanding place value:

  • In 247, the digit 2 is in the hundreds place, so it actually represents 2 groups of 100, which is 200
  • In 247, the digit 4 is in the tens place, so it represents 4 groups of 10, which is 40
  • In 247, the digit 7 is in the ones place, so it represents 7 individual units
  • So 247 means 200 + 40 + 7, not 2 + 4 + 7

Think of it this way: If you have 247 apples, you could group them as 2 groups of 100 apples (200 apples) plus 4 groups of 10 apples (40 apples) plus 7 individual apples. That's 200 + 40 + 7 = 247 apples total.

The position of each digit tells us its true value in the number!

Question: How do I know which digit is the hundreds, which is the tens, and which is the ones?

Answer: It's easy once you know the pattern:

  • Look at the number from left to right
  • The first digit (leftmost) is always the hundreds place
  • The second digit (middle) is always the tens place
  • The third digit (rightmost) is always the ones place

Examples:

  • In 123: 1 is hundreds, 2 is tens, 3 is ones
  • In 456: 4 is hundreds, 5 is tens, 6 is ones
  • In 789: 7 is hundreds, 8 is tens, 9 is ones

Remember: Hundreds comes first (left side), Tens comes second (middle), Ones comes third (right side).

Question: What happens if I add the expanded form back together? Should I get the original number?

Answer: Yes, absolutely! This is a great way to check your work!

When you write a number in expanded form, you're just showing how it's made up of its parts. So when you add those parts back together, you should get the original number:

  • 247 = 200 + 40 + 7 → 200 + 40 + 7 = 247 ✓
  • 385 = 300 + 80 + 5 → 300 + 80 + 5 = 385 ✓
  • 562 = 500 + 60 + 2 → 500 + 60 + 2 = 562 ✓

This is called the "check method" - always add your expanded parts to make sure they equal the original number. If they don't match, you made a mistake somewhere!

This helps you catch errors and confirms your understanding of place value.