Multiplying by 10: When you multiply any number by 10, you add a zero to the end of that number.
- 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 10 with 2-digit numbers: The same rule applies - add a zero to the end of the number.
We have 23 as our number
Add one zero to the end of 23
23 with a zero added at the end gives us 230
23 × 10 = 230
• Rule of 10: Adding a zero works for any number, regardless of size
• Place value: 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 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 with 2-digit numbers: Add one zero to the end of the number.
We have 42 as our number
Add one zero to the end of 42
42 with a zero added at the end gives us 420
42 × 10 = 420
• 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 single digits: Add one zero to the end of the number.
We have 8 as our number
Add one zero to the end of 8
8 with a zero added at the end gives us 80
8 × 10 = 80
• Rule of 10: Adding a zero to any number multiplies it by 10
• Place value: The ones digit becomes the tens digit
• Pattern recognition: All multiples of 10 end in zero
Multiplying by 10 with 2-digit numbers: Add one zero to the end of the number.
We have 15 as our number
Add one zero to the end of 15
15 with a zero added at the end gives us 150
15 × 10 = 150
• 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 6 as our number
Add two zeros to the end of 6
6 with two zeros added at the end gives us 600
6 × 100 = 600
• 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 2-digit numbers: Add one zero to the end of the number.
We have 34 as our number
Add one zero to the end of 34
34 with a zero added at the end gives us 340
34 × 10 = 340
• 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 2-digit numbers: Add one zero to the end of the number.
We have 78 as our number
Add one zero to the end of 78
78 with a zero added at the end gives us 780
78 × 10 = 780
• 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 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 multiplies by 100
• Place value: Each digit shifts two places left
• Pattern recognition: All multiples of 100 end in two zeros
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.
Multiplication by 10: Adding one zero to the end of any number
Multiplication by 100: Adding two zeros to the end of any number
Place value: The value of a digit based on its position in a number
- Identify the number: Look at the number you need to multiply
- Identify the multiplier: Determine if you're multiplying by 10, 100, etc.
- Apply the rule: Add the correct number of zeros to the end
- Write the answer: Form the final number with the added zeros
• Multiplying by 10: Add one zero to the end of the number
• Multiplying by 100: Add two zeros to the end of the number
• Place value shift: Each digit moves one place left when multiplying by 10
• Zero rule: Results always end in the number of zeros equal to the multiplier
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!