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.
- Take the original number (45)
- Add a zero at the end
- The result is 450
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 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 10 with 3-digit numbers: The same rule applies - add a zero to the end of the number.
We have 123 as our number
Add one zero to the end of 123
123 with a zero added at the end gives us 1230
123 × 10 = 1230
• Rule of 10: Adding a zero works for any number, regardless of size
• Place value: Hundreds become thousands, tens become hundreds, ones become tens
• 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.
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 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 with 2-digit numbers: Add one zero to the end of the number.
We have 67 as our number
Add one zero to the end of 67
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 with single digits: Add two zeros to the end of the number.
We have 9 as our number
Add two zeros to the end of 9
9 with two zeros added at the end gives us 900
9 × 100 = 900
• Rule of 100: Adding two zeros to any number multiplies it by 100
• Place value: The ones digit becomes the hundreds digit
• Pattern recognition: All multiples of 100 end in two zeros
Multiplying by 10 with 2-digit numbers: Add one zero to the end of the number.
We have 89 as our number
Add one zero to the end of 89
89 with a zero added at the end gives us 890
89 × 10 = 890
• Rule of 10: Adding a zero to any number multiplies it by 10
• Place value: Tens become hundreds, ones become tens
• Pattern recognition: All multiples of 10 end in zero
Multiplying by 100: Add two zeros to the end of the number.
We have 45 as our number
Add two zeros to the end of 45
45 with two zeros added at the end gives us 4500
45 × 100 = 4500
• 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 with 3-digit numbers: Add one zero to the end of the number.
We have 234 as our number
Add one zero to the end of 234
234 with a zero added at the end gives us 2340
234 × 10 = 2340
• 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 10 with 3-digit numbers: Add one zero to the end of the number.
We have 567 as our number
Add one zero to the end of 567
567 with a zero added at the end gives us 5670
567 × 10 = 5670
• 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: Add two zeros to the end of the number.
We have 78 as our number
Add two zeros to the end of 78
78 with two zeros added at the end gives us 7800
78 × 100 = 7800
• 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
- n × 100 = n with two zeros added at the end
- All multiples of 10 end in 0
- All multiples of 100 end in 00
- When multiplying by 10: ones become tens, tens become hundreds, hundreds become thousands
- When multiplying by 100: ones become hundreds, tens become thousands, hundreds become ten-thousands
- Identify the number you want to multiply
- Determine if you're multiplying by 10, 100, or another power of 10
- Add the correct number of zeros to the end of the number
- Count the zeros in your answer to verify correctness
- 5 × 10 = 50
- 3 × 100 = 300
- 7 × 10 = 70
- 45 × 10 = 450
- 123 × 10 = 1230
- 67 × 100 = 6700
- 234 × 10 = 2340
- Always count the zeros in your answer to make sure they match the multiplier
- Think of it as shifting digits to the left in place value
- Practice with small numbers first, then move to larger ones
- Remember: multiplying by 10 adds one zero, multiplying by 100 adds two zeros
- 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
- "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
Add one zero to the end of the number
Add two zeros to the end of the number
When multiplying by 10, each digit moves one place to the left.
When multiplying by 100, each digit moves two places to the left.
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!