Multiplying by 10: When multiplying any number by 10, add a zero to the end of the number.
- Take the original number (7)
- Add a zero to the end (7 becomes 70)
- The result is 70
Step 1: Identify the number to multiply
We have the number 7
Step 2: Apply the rule for multiplying by 10
When multiplying by 10, we add one zero to the end of the number
Step 3: Calculate the result
7 with a zero added to the end becomes 70
7 × 10 = 70
• Adding a zero: Multiplying any number by 10 adds one zero to the end
• Place value shift: Each digit moves one place to the left
• Pattern recognition: The result is always the original number followed by 0
Multiplying two-digit numbers by 10: The same rule applies - add a zero to the end of the entire number.
Step 1: Identify the number to multiply
We have the two-digit number 24
Step 2: Apply the rule for multiplying by 10
Add a zero to the end of the entire number (not just the last digit)
Step 3: Calculate the result
24 with a zero added to the end becomes 240
24 × 10 = 240
• Whole number rule: Add zero to the entire number, not just the units digit
• Place value shift: Tens become hundreds, ones become tens
• Common mistake: Don't just add zero to the units place separately
Multiplying three-digit numbers by 10: The pattern continues - add a zero to the end of the entire number.
Step 1: Identify the number to multiply
We have the three-digit number 135
Step 2: Apply the rule for multiplying by 10
Add a zero to the end of the entire number
Step 3: Calculate the result
135 with a zero added to the end becomes 1350
135 × 10 = 1350
• Consistent rule: Adding one zero works for any number of digits
• Place value movement: Hundreds become thousands, tens become hundreds, ones become tens
• Zero placement: Always add the zero at the end of the complete number
Rule: Adding Zero When Multiplying by 10
When you multiply any whole number by 10, simply add one zero to the end of that number.
Single Digit Examples
Two Digit Examples
Three Digit Examples
Why This Works
When multiplying by 10, each digit shifts one place to the left in the place value system. The ones become tens, tens become hundreds, etc. The zero fills the empty ones place.
Place Value Understanding
24 = 2 tens + 4 ones
24 × 10 = 2 hundreds + 4 tens + 0 ones = 240
Easy Problems
Medium Problems
Harder Problems
Tips for Success
- Always add the zero at the end of the complete number
- Don't change any digits in the original number
- Count the digits to make sure you have the right number of digits in your answer
- Check your work by dividing by 10 to get back to the original number
Common Mistakes to Avoid
- Adding the zero in the middle of the number
- Changing digits while adding the zero
- Forgetting to add the zero completely
- Adding multiple zeros instead of just one
Memory Trick
"Multiply by 10, add a zero at the end!"
Core Concept: Place Value Shift
When multiplying by 10, each digit moves one place to the left in the place value chart.
Place Value: The value of a digit based on its position in a number
Multiplication by 10: A mathematical operation that increases a number by a factor of 10
Decimal System: Our base-10 number system where each place represents a power of 10
- Introduce the concept: Explain what happens when we multiply by 10
- Show the pattern: Demonstrate with multiple examples
- Practice the rule: Have students apply the "add zero" rule
- Connect to place value: Explain why the rule works
- Provide varied practice: Different number sizes and contexts
• Every whole number multiplied by 10 ends in zero
• The number of digits increases by one when multiplying by 10
• Each digit moves one place to the left in the place value chart
• The result is always 10 times larger than the original number
• This pattern continues for larger multiples of 10 (×100, ×1000, etc.)
Connection to Other Operations
Multiplying by 10 is the inverse of dividing by 10. Understanding this relationship helps students develop number sense and prepares them for more complex operations.
Questions & Answers
Question: How do I help my students understand WHY multiplying by 10 adds a zero, rather than just memorizing the rule?
Answer: Excellent question! Building conceptual understanding is crucial:
- Use base-10 blocks to show that 10 ones become 1 ten, 10 tens become 1 hundred
- Create place value charts where students can see digits shifting positions
- Relate to grouping: 5 groups of 10 is 50, which is 5 tens
- Use real-world examples: 3 dollars is 30 dimes (3 × 10)
For example, with 4 × 10: Show that 4 ones become 4 tens, which we write as 40. The zero represents that there are 0 ones in the final number.
Question: My child sometimes forgets to add the zero or adds it in the wrong place. How can I help them remember the correct procedure?
Answer: Try these memory aids and practice techniques:
- Create a memory phrase: "Multiply by 10, add a zero at the END!"
- Use finger tracking: Have them point to each digit and then add the zero at the far right
- Practice with visual cues: Circle the original number, then draw an arrow to add the zero
- Start with simple problems and gradually increase complexity
Also encourage them to check their work: if 7 × 10 = 70, then 70 ÷ 10 should equal 7. This builds confidence and reinforces the concept.
Question: Why does multiplying by 10 make the number bigger? And why do we add a zero?
Answer: Great thinking! Here's why:
- When you multiply by 10, you're taking the original number and having 10 groups of it
- If you have 1 group of 3 (which is 3), then 10 groups of 3 is 30 - much bigger!
- We add a zero because our number system is based on 10s (called base-10)
- Each place value is 10 times bigger than the one before it (ones, tens, hundreds...)
Think of it like this: 4 people become 40 when there are 10 groups of 4 people. That's why we write it as 40 with a zero!