Place value shift: When multiplying by 10, each digit moves one place to the left
- Identify the original number (4)
- Recognize that multiplying by 10 shifts digits one place left
- Add a zero in the ones place
- Result: 4 × 10 = 40
4 is in the ones place
Each digit moves one place to the left
4 moves from ones to tens place, zero fills ones
4 × 10 = 40
When you multiply 4 by 10, you get 40.
Explanation: The digit 4 moves from the ones place to the tens place, and a zero fills the ones place.
• Place value shift: Each digit moves one place to the left when multiplying by 10
• Zero insertion: A zero is added in the ones place after shifting
• Value multiplication: The number becomes 10 times larger
Two-digit multiplication: Each digit in the number moves one place to the left when multiplied by 10
2 is in the tens place, 3 is in the ones place
Each digit moves one place to the left
2 moves from tens to hundreds place, 3 moves from ones to tens place
Zero fills the empty ones place
23 × 10 = 230
When you multiply 23 by 10, you get 230.
Explanation: Each digit moves one place to the left. The 2 moves from tens to hundreds place, the 3 moves from ones to tens place, and a zero fills the ones place.
• Place value shift: Each digit moves one place to the left when multiplying by 10
• Zero insertion: A zero is added in the ones place after shifting
• Value multiplication: The number becomes 10 times larger
Grouping by tens: Multiplying by 10 creates groups of ten
Imagine you have 5 separate groups
Each group contains 10 items
Group 1: 10, Group 2: 10, Group 3: 10, Group 4: 10, Group 5: 10
10 + 10 + 10 + 10 + 10 = 50
5 × 10 = 50
When you multiply 5 by 10, you get 50.
Explanation: This is the same as having 5 groups of 10, which equals 50.
• Repeated addition: 5 × 10 = 10 + 10 + 10 + 10 + 10
• Grouping: Multiplication is repeated addition of equal groups
• Value multiplication: The number becomes 10 times larger
Multiplying by 10: A mathematical operation that increases a number's value by a factor of 10
Place value: The value of a digit based on its position in a number
Digit shift: Moving digits to the left when multiplying by 10
Repeated addition: Multiplication as adding the same number multiple times
- Identify the number: Recognize the number being multiplied
- Shift digits: Move each digit one place to the left
- Add zero: Place a zero in the rightmost position
- Verify: Check that the result is 10 times larger
Three-digit multiplication: Each digit in the number moves one place to the left when multiplied by 10
3 is in the hundreds place, 4 is in the tens place, 7 is in the ones place
Each digit moves one place to the left
3 moves from hundreds to thousands place, 4 moves from tens to hundreds place, 7 moves from ones to tens place
Zero fills the empty ones place
347 × 10 = 3470
When you multiply 347 by 10, you get 3470.
Explanation: Each digit moves one place to the left. The 3 moves from hundreds to thousands place, the 4 moves from tens to hundreds place, the 7 moves from ones to tens place, and a zero fills the ones place.
• Place value shift: Each digit moves one place to the left when multiplying by 10
• Zero insertion: A zero is added in the ones place after shifting
• Value multiplication: The number becomes 10 times larger
Real-world multiplication: Applying multiplication by 10 to practical scenarios
One book costs $6
We want 10 books
6 moves from ones to tens place, zero fills ones place
6 × 10 = 60, so 10 books cost $60
Ten books would cost $60.
Explanation: Using place value, when you multiply $6 by 10, the 6 moves from the ones place to the tens place, and a zero fills the ones place, giving $60.
• Place value shift: Each digit moves one place to the left when multiplying by 10
• Real-world context: Applying mathematical concepts to practical problems
• Value multiplication: The cost becomes 10 times larger
Multiplying by 10: A mathematical operation that increases a number's value by a factor of 10.
Place value: The value of a digit based on its position in a number (ones, tens, hundreds, etc.).
Digit shift: Moving digits one position to the left when multiplying by 10.
Zero insertion: Adding a zero in the ones place after multiplying by 10.
Value multiplication: The result is always 10 times larger than the original number.
• Place value shift: Each digit moves one place to the left when multiplying by 10.
• Zero addition: A zero is always added in the rightmost position.
• Value increase: The result is always 10 times the original number.
• Position importance: The position of each digit determines its value.
1. Identify the number: Recognize the number you want to multiply by 10.
2. Shift digits left: Move each digit one place value to the left.
3. Add zero: Place a zero in the ones place after shifting.
4. Verify result: Check that the number is 10 times larger.
5. Apply context: Use the result in the problem's context.
Simple: 1 × 10 = 10 (1 moves from ones to tens, zero fills ones)
Basic: 5 × 10 = 50 (5 moves from ones to tens, zero fills ones)
Intermediate: 23 × 10 = 230 (2 moves from tens to hundreds, 3 moves from ones to tens, zero fills ones)
Advanced: 456 × 10 = 4560 (4 moves from hundreds to thousands, 5 moves from tens to hundreds, 6 moves from ones to tens, zero fills ones)
• Quick method: Simply add a zero to the end of the number.
• Visual aid: Imagine moving each digit one place to the left.
• Check work: Divide your answer by 10 to see if you get the original number.
• Understand why: Each place value is 10 times larger than the previous one.
• Forgetting to add the zero in the ones place after shifting digits
• Confusing which direction to shift digits (always left)
• Misunderstanding that the number becomes 10 times larger, not just bigger by 10
• Not recognizing that place value changes the value of each digit
• Multiplying by 10 always adds one zero to the end of the number
• Each digit moves one place value to the left (ones → tens → hundreds)
• The result is always 10 times the original number
• This works for any number, regardless of how many digits it has
• Understanding place value is key to mastering this concept
Questions & Answers
Question: Why does multiplying by 10 always add a zero to the end of the number?
Answer: This happens because of our base-10 number system:
- Our number system has 10 digits (0-9)
- Each place value is 10 times larger than the one to its right
- When you multiply by 10, each digit moves to a place value that's 10 times larger
- The ones place becomes empty, so we fill it with zero
Example: 24 × 10 → 2 moves from tens to hundreds, 4 moves from ones to tens, zero fills the empty ones place = 240
Question: What happens if I multiply a number like 10 by 10? Do I add two zeros?
Answer: No, you still only add one zero when multiplying by 10:
- 10 × 10 = 100 (not 1000)
- Each digit moves one place to the left
- The 1 moves from tens to hundreds place
- The 0 moves from ones to tens place
- A new zero fills the empty ones place
Remember: You multiply by 10 once, so you add one zero, regardless of how many zeros were in the original number.
Question: Can I multiply by 10 the same way with really big numbers?
Answer: Yes! The same rule applies to any number, no matter how big:
- Every digit moves one place to the left
- A zero is added in the ones place
- The result is always 10 times larger than the original
Examples: 123 × 10 = 1230, 4567 × 10 = 45670, 89012 × 10 = 890120
The pattern is always the same: shift left, add zero!