Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number, shifting all digits one place to the left in the place value system.
- Take the original number (7)
- Add a zero at the end
- The result is 70
We have 7 as our number
When multiplying by 10, we add one zero to the end of the number
7 with a zero added at the end gives us 70
7 × 10 = 70
• Rule of 10: Adding a zero to any number multiplies it by 10
• Place value: Each digit moves one place to the left
• Pattern recognition: All multiples of 10 end in zero
Multiplying by 100: When you multiply any number by 100, you add two zeros to the end of that number, shifting all digits two places to the left in the place value system.
We have 5 as our number
When multiplying by 100, we add two zeros to the end of the number
5 with two zeros added at the end gives us 500
5 × 100 = 500
• Rule of 100: Adding two zeros to any number multiplies it by 100
• Place value: Each digit moves two places to the left
• Pattern recognition: All multiples of 100 end in two zeros
Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number, shifting all digits one place to the left.
We have 23 as our number
When multiplying by 10, we add one zero to the end of the number
23 with a zero added at the end gives us 230
23 × 10 = 230
• Rule of 10: Adding a zero works for any number
• Place value: Each digit shifts one place left
• Pattern recognition: Result ends in zero
Multiplying by 100: When you multiply any number by 100, you add two zeros to the end of that number.
We have 12 as our number
When multiplying by 100, we add two zeros to the end of the number
12 with two zeros added at the end gives us 1200
12 × 100 = 1200
• Rule of 100: Adding two zeros multiplies by 100
• Place value: Each digit shifts two places left
• Pattern recognition: All multiples of 100 end in two zeros
Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number.
We have 45 as our number
When multiplying by 10, we add one zero to the end of the number
45 with a zero added at the end gives us 450
45 × 10 = 450
• Rule of 10: Adding a zero works for any number
• Place value: Each digit shifts one place left
• Pattern recognition: Result ends in zero
Multiplying by 100: When you multiply any number by 100, you add two zeros to the end of that number.
We have 34 as our number
When multiplying by 100, we add two zeros to the end of the number
34 with two zeros added at the end gives us 3400
34 × 100 = 3400
• Rule of 100: Adding two zeros multiplies by 100
• Place value: Each digit shifts two places left
• Pattern recognition: All multiples of 100 end in two zeros
Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number.
We have 9 as our number
When multiplying by 10, we add one zero to the end of the number
9 with a zero added at the end gives us 90
9 × 10 = 90
• Rule of 10: Adding a zero works for any number
• Place value: Each digit shifts one place left
• Pattern recognition: Result ends in zero
Multiplying by 100: When you multiply any number by 100, you add two zeros to the end of that number.
We have 8 as our number
When multiplying by 100, we add two zeros to the end of the number
8 with two zeros added at the end gives us 800
8 × 100 = 800
• Rule of 100: Adding two zeros multiplies by 100
• Place value: Each digit shifts two places left
• Pattern recognition: All multiples of 100 end in two zeros
Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number.
We have 67 as our number
When multiplying by 10, we add one zero to the end of the number
67 with a zero added at the end gives us 670
67 × 10 = 670
• Rule of 10: Adding a zero works for any number
• Place value: Each digit shifts one place left
• Pattern recognition: Result ends in zero
Multiplying by 100: When you multiply any number by 100, you add two zeros to the end of that number.
We have 89 as our number
When multiplying by 100, we add two zeros to the end of the number
89 with two zeros added at the end gives us 8900
89 × 100 = 8900
• Rule of 100: Adding two zeros multiplies by 100
• Place value: Each digit shifts two places left
• Pattern recognition: All multiples of 100 end in two zeros
- n × 10 = n with one zero added at the end
- Each digit moves one place to the left
- Ones become tens, tens become hundreds
- n × 100 = n with two zeros added at the end
- Each digit moves two places to the left
- Ones become hundreds, tens become thousands
- n × 10^k = n with k zeros added at the end
- Each digit moves k places to the left
- Take the original number
- Add one zero at the end
- Each digit has moved one place to the left
- The result is the answer
- Take the original number
- Add two zeros at the end
- Each digit has moved two places to the left
- The result is the answer
- 5 × 10 = 50 (5 moves from ones to tens place)
- 23 × 10 = 230 (2 moves from tens to hundreds, 3 moves from ones to tens)
- 456 × 10 = 4560 (each digit moves one place left)
- 7 × 10 = 70 (7 moves from ones to tens place)
- 3 × 100 = 300 (3 moves from ones to hundreds place)
- 12 × 100 = 1200 (1 moves from tens to thousands, 2 moves from ones to hundreds)
- 45 × 100 = 4500 (each digit moves two places left)
- 7 × 100 = 700 (7 moves from ones to hundreds place)
- Count the zeros in the multiplier to know how many zeros to add
- Think of it as shifting digits to the left in place value
- Remember: multiplying by 10 adds one zero, multiplying by 100 adds two zeros
- Check your answer by counting the zeros in the result
- Adding the wrong number of zeros (e.g., adding two zeros when multiplying by 10)
- Forgetting to keep the original digits intact
- Mixing up the rules for 10 and 100
- Not understanding that digits shift positions, not just zeros are added
- "Multiply by 10, add one zero"
- "Multiply by 100, add two zeros"
- Each digit moves left in place value
- The number of zeros in the answer matches the number of zeros in the multiplier
- Our number system is based on groups of 10
Add one zero to the end of the number
Add two zeros to the end of the number
• Adds one zero
• Digits shift one place left
• Ones → Tens
• Tens → Hundreds
• Adds two zeros
• Digits shift two places left
• Ones → Hundreds
• Tens → Thousands
| Multiplication | Rule Applied | Result |
|---|---|---|
| 5 × 10 | Add one zero | 50 |
| 7 × 100 | Add two zeros | 700 |
| 12 × 10 | Add one zero | 120 |
| 23 × 100 | Add two zeros | 2300 |
| 4 × 10 | Add one zero | 40 |
| 6 × 100 | Add two zeros | 600 |
| 34 × 10 | Add one zero | 340 |
| 56 × 100 | Add two zeros | 5600 |
Questions & Answers
Question: Why does multiplying by 10 just add a zero? It seems too easy!
Answer: That's a great observation! It might seem too easy, but there's an important mathematical principle behind it. When you multiply by 10, you're essentially shifting each digit one place to the left in the place value system.
For example, in the number 5: the 5 is in the ones place. When you multiply by 10, the 5 moves to the tens place, and a 0 takes the ones place: 50.
This pattern continues with larger numbers: 23 becomes 230 because the 2 moves from tens to hundreds, the 3 moves from ones to tens, and a 0 fills the ones place.
It's a shortcut that works because of how our base-10 number system is designed!
Question: My child is struggling with the concept of multiplying by 100. How can I help them understand the difference between multiplying by 10 and 100?
Answer: A helpful way to teach the difference is through visualization and patterns:
- Explain that multiplying by 10 adds ONE zero (because 10 has one zero)
- Explain that multiplying by 100 adds TWO zeros (because 100 has two zeros)
- Show the pattern: 3 × 10 = 30, but 3 × 100 = 300
You can also use place value blocks or draw place value charts to show how digits shift positions:
- When multiplying by 10: ones become tens, tens become hundreds
- When multiplying by 100: ones become hundreds, tens become thousands
Practice with visual aids like number lines or base-10 blocks to reinforce the concept.
Question: What happens if I multiply by 1,000? Do I add three zeros?
Answer: Yes, exactly! You've discovered the pattern! When multiplying by 1,000, you add three zeros to the end of the number.
Here's the pattern:
- Multiplying by 10: add 1 zero (10 has one zero)
- Multiplying by 100: add 2 zeros (100 has two zeros)
- Multiplying by 1,000: add 3 zeros (1,000 has three zeros)
So for example: 4 × 1,000 = 4,000
This pattern continues: multiplying by 10,000 would add four zeros, and so on. The number of zeros you add always matches the number of zeros in the multiplier!