Show how many tens and ones are in 47.
Expanded form: Writing a number as the sum of its place values. For 2-digit numbers: tens + ones
- Identify the digit in the tens place
- Identify the digit in the ones place
- Write the tens value as (digit × 10)
- Write the ones value as (digit × 1)
- Add them together
In 47: TENS = 4, ONES = 7
4 tens = 4 × 10 = 40
7 ones = 7 × 1 = 7
47 = 40 + 7
47 in expanded form is 40 + 7
47 has 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
• Tens rule: Tens digit × 10 gives the tens value
• Ones rule: Ones digit × 1 gives the ones value
Break down 562 into hundreds, tens and ones.
Number decomposition: Breaking a number into its component parts based on place value
In 562: HUNDREDS = 5, TENS = 6, ONES = 2
5 hundreds = 5 × 100 = 500
6 tens = 6 × 10 = 60
2 ones = 2 × 1 = 2
562 = 500 + 60 + 2
562 in expanded form is 500 + 60 + 2
562 has 5 hundreds, 6 tens and 2 ones
• 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
Show the relationship between digits and their values.
Place value relationship: The position of a digit determines its actual value in the number
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
• 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
Hundred Thousands: The leftmost digit in a 6-digit number, worth 100,000 times its face value
Ten Thousands: The second digit in a 6-digit number, worth 10,000 times its face value
Thousands: The third digit in a 6-digit number, worth 1,000 times its face value
Hundreds: The fourth digit in a 6-digit number, worth 100 times its face value
Tens: The fifth digit in a 6-digit number, worth 10 times its face value
Ones: The sixth digit in a 6-digit number, worth its face value
- Identify positions: Recognize all place value positions
- Extract digits: Separate each digit from its position
- Calculate values: Multiply each digit by its place value multiplier
- Write expanded form: Express as sum of place values
• Left digit: Always represents the highest place value
• Each position: Worth 10 times the position to its right
• Value calculation: Digit × its place value multiplier
• Expanded form: Sum of calculated place values
• Verification: Adding expanded parts should equal original number
Show how 532,478 is composed of hundred thousands, ten thousands, thousands, hundreds, tens and ones.
Number composition: Understanding how digits combine to form a whole number
In 532,478: HUNDRED THOUSANDS = 5, TEN THOUSANDS = 3, THOUSANDS = 2, HUNDREDS = 4, TENS = 7, ONES = 8
5 hundred thousands = 5 × 100,000 = 500,000
3 ten thousands = 3 × 10,000 = 30,000
2 thousands = 2 × 1,000 = 2,000
4 hundreds = 4 × 100 = 400
7 tens = 7 × 10 = 70
8 ones = 8 × 1 = 8
532,478 = 500,000 + 30,000 + 2,000 + 400 + 70 + 8
532,478 in expanded form is 500,000 + 30,000 + 2,000 + 400 + 70 + 8
532,478 has 5 hundred thousands, 3 ten thousands, 2 thousands, 4 hundreds, 7 tens and 8 ones
• Position identification: Leftmost digit is hundred 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 in maths, 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 the expanded form
- Add the expanded parts
- Check if result equals the 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.