Show how many thousands, hundreds, tens and ones are in 3,247.
Expanded form: Writing a number as the sum of its place values. For 4-digit numbers: thousands + hundreds + tens + ones
- Identify the digit in the thousands place
- Identify the digit in the hundreds place
- Identify the digit in the tens place
- Identify the digit in the ones place
- Write the thousands value as (digit × 1000)
- Write the hundreds value as (digit × 100)
- Write the tens value as (digit × 10)
- Write the ones value as (digit × 1)
- Add them together
In 3,247: THOUSANDS = 3, HUNDREDS = 2, TENS = 4, ONES = 7
3 thousands = 3 × 1000 = 3000
2 hundreds = 2 × 100 = 200
4 tens = 4 × 10 = 40
7 ones = 7 × 1 = 7
3,247 = 3000 + 200 + 40 + 7
3,247 in expanded form is 3000 + 200 + 40 + 7
3,247 has 3 thousands, 2 hundreds, 4 tens and 7 ones
• Place value rule: Each digit's value depends on its position
• Expanded form rule: Add the values of each place
• Thousands rule: Thousands digit × 1000 gives the thousands value
• 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
Break down 4,856 into thousands, hundreds, tens and ones.
Number decomposition: Breaking a number into its component parts based on place value
In 4,856: THOUSANDS = 4, HUNDREDS = 8, TENS = 5, ONES = 6
4 thousands = 4 × 1000 = 4000
8 hundreds = 8 × 100 = 800
5 tens = 5 × 10 = 50
6 ones = 6 × 1 = 6
4,856 = 4000 + 800 + 50 + 6
4,856 in expanded form is 4000 + 800 + 50 + 6
4,856 has 4 thousands, 8 hundreds, 5 tens and 6 ones
• Place value identification: Leftmost digit is thousands, then hundreds, tens, then ones
• Value calculation: Thousands × 1000, Hundreds × 100, Tens × 10, Ones × 1
• Addition principle: Combine place values with addition
Show the relationship between digits and their values.
Place value relationship: The position of a digit determines its actual value in the number
In 7,632: THOUSANDS = 7, HUNDREDS = 6, TENS = 3, ONES = 2
7 thousands = 7 × 1000 = 7000
6 hundreds = 6 × 100 = 600
3 tens = 3 × 10 = 30
2 ones = 2 × 1 = 2
7,632 = 7000 + 600 + 30 + 2
7,632 in expanded form is 7000 + 600 + 30 + 2
7,632 has 7 thousands, 6 hundreds, 3 tens and 2 ones
• Position matters: Thousands place is worth 1000 times the digit
• Hundreds place: 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: The value of a digit based on its position in a number
Expanded form: Writing a number as the sum of its place values
Thousands: The leftmost digit in a 4-digit number, worth 1000 times its face value
Hundreds: The second digit in a 4-digit number, worth 100 times its face value
Tens: The third digit in a 4-digit number, worth 10 times its face value
Ones: The fourth digit in a 4-digit number, worth its face value
- Identify positions: Recognize thousands, hundreds, tens and ones places
- Extract digits: Separate the thousands, hundreds, tens and ones digits
- Calculate values: Multiply thousands by 1000, hundreds by 100, tens by 10, ones by 1
- Write expanded form: Express as sum of place values
• Left digit: Always represents thousands in 4-digit numbers
• Second digit: Always represents hundreds in 4-digit numbers
• Third digit: Always represents tens in 4-digit numbers
• Right digit: Always represents ones in 4-digit numbers
• Value calculation: Thousands digit × 1000, Hundreds digit × 100, Tens digit × 10, Ones digit × 1
• Expanded form: Sum of calculated place values
• Verification: Adding expanded parts should equal original number
Show how 53,247 is composed of ten thousands, thousands, hundreds, tens and ones.
Number composition: Understanding how digits combine to form a whole number
In 53,247: TEN THOUSANDS = 5, THOUSANDS = 3, HUNDREDS = 2, TENS = 4, ONES = 7
5 ten thousands = 5 × 10,000 = 50,000
3 thousands = 3 × 1,000 = 3,000
2 hundreds = 2 × 100 = 200
4 tens = 4 × 10 = 40
7 ones = 7 × 1 = 7
53,247 = 50,000 + 3,000 + 200 + 40 + 7
53,247 in expanded form is 50,000 + 3,000 + 200 + 40 + 7
53,247 has 5 ten thousands, 3 thousands, 2 hundreds, 4 tens and 7 ones
• Position identification: Leftmost digit is ten thousands place
• Value multiplication: Each digit multiplied by its place value
• Summation: Add place values to form expanded notation
Demonstrate complete understanding of place value.
Place value mastery: Understanding how each position contributes to the overall number value
In 9,876,543: MILLIONS = 9, HUNDRED THOUSANDS = 8, TEN THOUSANDS = 7, THOUSANDS = 6, HUNDREDS = 5, TENS = 4, ONES = 3
9 millions = 9 × 1,000,000 = 9,000,000
8 hundred thousands = 8 × 100,000 = 800,000
7 ten thousands = 7 × 10,000 = 70,000
6 thousands = 6 × 1,000 = 6,000
5 hundreds = 5 × 100 = 500
4 tens = 4 × 10 = 40
3 ones = 3 × 1 = 3
9,876,543 = 9,000,000 + 800,000 + 70,000 + 6,000 + 500 + 40 + 3
9,876,543 in expanded form is 9,000,000 + 800,000 + 70,000 + 6,000 + 500 + 40 + 3
9,876,543 has 9 millions, 8 hundred thousands, 7 ten thousands, 6 thousands, 5 hundreds, 4 tens and 3 ones
• 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
This comprehensive summary covers all aspects of expanded form for grade 1 students, providing clear explanations, methods, and examples for mastering place value concepts including ones, tens, hundreds, thousands, ten thousands, and hundred thousands.
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., 532,478 = 500,000 + 30,000 + 2,000 + 400 + 70 + 8).
Ones Place: The rightmost position in a number, worth the digit's face value.
Tens Place: The second position from the right, worth 10 times the digit's face value.
Hundreds Place: The third position from the right, worth 100 times the digit's face value.
Thousands Place: The fourth position from the right, worth 1,000 times the digit's face value.
Ten Thousands Place: The fifth position from the right, worth 10,000 times the digit's face value.
Hundred Thousands Place: The sixth position from the right, worth 100,000 times 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.
Position Rule: Each position in a number has a specific value that is 10 times the value of the position to its right.
Value Rule: Each digit's value = digit × its place value multiplier.
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 number regardless of size.
Method 1: Standard Approach
- Identify the digit in each place value position
- Determine the place value multiplier for each position
- Multiply each digit by its place value multiplier
- Add all the calculated values together
Method 2: Verification Approach
- Write expanded form
- Add the expanded parts
- Check if result equals original number
Simple Examples:
25 = 20 + 5 (2 tens + 5 ones)
347 = 300 + 40 + 7 (3 hundreds + 4 tens + 7 ones)
Intermediate Examples:
2,534 = 2000 + 500 + 30 + 4 (2 thousands + 5 hundreds + 3 tens + 4 ones)
47,683 = 40,000 + 7,000 + 600 + 80 + 3 (4 ten thousands + 7 thousands + 6 hundreds + 8 tens + 3 ones)
Advanced Examples:
532,478 = 500,000 + 30,000 + 2,000 + 400 + 70 + 8 (5 hundred thousands + 3 ten thousands + 2 thousands + 4 hundreds + 7 tens + 8 ones)
9,876,543 = 9,000,000 + 800,000 + 70,000 + 6,000 + 500 + 40 + 3 (9 millions + 8 hundred thousands + 7 ten thousands + 6 thousands + 5 hundreds + 4 tens + 3 ones)
Tips:
- Each position is worth 10 times the position to its right
- Always write expanded form with addition signs (+)
- Check by adding expanded parts
- Remember the sequence: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions
Common Mistakes:
- Forgetting to multiply by the correct place value
- Confusing digit positions
- Omitting addition signs in expanded form
Memory Aids:
- "Ones are ones!" - They stay as themselves
- "Tens are ten times!" - They multiply by 10
- "Hundreds are hundred times!" - They multiply by 100
- "Thousands are thousand times!" - They multiply by 1,000
- "Each position is 10 times the next smaller position"
Quick Check: Always add expanded parts to verify your answer equals the original number.
Pattern Recognition: Each place value is a power of 10: 1, 10, 100, 1,000, 10,000, 100,000, etc.
Questions & Answers
Question: I don't understand why 47 becomes 40 + 7. Why isn't it just 4 + 7?
Answer: Great question! The key is understanding place value:
- In 47, the digit 4 is in the tens place, so it actually represents 4 groups of 10, which is 40
- In 47, the digit 7 is in the ones place, so it represents 7 individual units
- So 47 means 40 + 7, not 4 + 7
Think of it this way: If you have 47 apples, you could group them as 4 groups of 10 apples (40 apples) plus 7 individual apples. That's 40 + 7 = 47 apples total.
The position of each digit tells us its true value in the number!
Question: How do I know which digit is the thousands, which 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
- Count the positions from the right
- The rightmost digit is the ones place
- The second from right is the tens place
- The third from right is the hundreds place
- The fourth from right is the thousands place
Examples:
- In 1,234: 1 is thousands, 2 is hundreds, 3 is tens, 4 is ones
- In 5,678: 5 is thousands, 6 is hundreds, 7 is tens, 8 is ones
- In 9,876: 9 is thousands, 8 is hundreds, 7 is tens, 6 is ones
Remember: Count positions from the right side of the number!
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:
- 47 = 40 + 7 → 40 + 7 = 47 ✓
- 562 = 500 + 60 + 2 → 500 + 60 + 2 = 562 ✓
- 3,247 = 3000 + 200 + 40 + 7 → 3000 + 200 + 40 + 7 = 3,247 ✓
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.