Multiplying by 10: A multiplication operation where one factor is 10
- Take the original number (7)
- Move each digit one place to the left
- Add a zero in the ones place
- Result: 7 × 10 = 70
We want to multiply 7 by 10
Multiplying by 10 means we have 10 groups of the number
When multiplying by 10, each digit moves one place to the left
The 7 moves from ones place to tens place, zero fills the ones place
7 × 10 = 70
When you multiply 7 by 10, you get 70.
Explanation: The digit 7 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 by 10: Each digit in the number moves one place to the left when multiplied by 10
In 24: 2 is in tens place, 4 is in ones place
24 × 10 means 10 groups of 24
2 moves from tens to hundreds place, 4 moves from ones to tens place
Zero fills the empty ones place after shifting
24 × 10 = 240
When you multiply 24 by 10, you get 240.
Explanation: The digit 2 moves from tens place to hundreds place, the digit 4 moves from ones place 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
Three-digit multiplication by 10: Each digit in the number moves one place to the left when multiplied by 10
In 365: 3 is in hundreds place, 6 is in tens place, 5 is in ones place
365 × 10 means 10 groups of 365
3 moves from hundreds to thousands place, 6 moves from tens to hundreds place, 5 moves from ones to tens place
Zero fills the empty ones place after shifting
365 × 10 = 3650
When you multiply 365 by 10, you get 3650.
Explanation: Each digit moves one place to the left: 3 from hundreds to thousands, 6 from tens to hundreds, 5 from ones to tens, and 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
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
Base 10 system: Our number system based on groups of 10
Expanded form: Writing numbers to show place value (e.g., 24 = 20 + 4)
- Identify the number: Recognize the number being multiplied by 10
- 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
Decimal multiplication by 10: Moving the decimal point one place to the right
We want to multiply $3.50 by 10
In $3.50: 3 is in ones place, 5 is in tenths place, 0 is in hundredths place
When multiplying by 10, move the decimal point one place to the right
3 moves from ones to tens place, 5 moves from tenths to ones place, 0 moves from hundredths to tenths place
$3.50 × 10 = $35.00
When you multiply $3.50 by 10, you get $35.00.
Explanation: The decimal point moves one place to the right, making the number 10 times larger.
• Decimal shift: Move decimal point one place to the right when multiplying by 10
• Value multiplication: The number becomes 10 times larger
• Money context: Same rules apply to monetary amounts
Large number multiplication by 10: Each digit in the number moves one place to the left when multiplied by 10
In 4,287: 4 is in thousands place, 2 is in hundreds place, 8 is in tens place, 7 is in ones place
4,287 × 10 means 10 groups of 4,287
4 moves from thousands to ten-thousands place, 2 moves from hundreds to thousands place, 8 moves from tens to hundreds place, 7 moves from ones to tens place
Zero fills the empty ones place after shifting
4,287 × 10 = 42,870
When you multiply 4,287 by 10, you get 42,870.
Explanation: Each digit moves one place to the left: 4 from thousands to ten-thousands, 2 from hundreds to thousands, 8 from tens to hundreds, 7 from ones to tens, and 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
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 each digit one place to the left when multiplying by 10.
Base 10 system: Our number system based on groups of 10.
Decimal point movement: Moving the decimal point one place to the right when multiplying decimals by 10.
• 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.
• Decimal movement: Move decimal point one place to the right for decimal numbers.
• Value multiplication: The result is always 10 times larger than the original number.
1. Identify the number: Recognize the number being multiplied by 10.
2. Understand place value: Know the position of each digit.
3. Shift digits: Move each digit one place to the left.
4. Add zero: Place a zero in the ones place after shifting.
5. Verify result: Check that the number is 10 times larger.
Simple: 1 × 10 = 10 (1 moves from ones to tens place, zero fills ones)
Basic: 5 × 10 = 50 (5 moves from ones to tens place, zero fills ones)
Intermediate: 24 × 10 = 240 (2 moves from tens to hundreds, 4 moves from ones to tens, zero fills ones)
Advanced: 365 × 10 = 3650 (3 moves from hundreds to thousands, 6 from tens to hundreds, 5 from ones to tens, zero fills ones)
Complex: $3.50 × 10 = $35.00 (decimal point moves one place right)
• 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!