Multiplying a decimal by 10: When you multiply a decimal by 10, you move the decimal point one place to the right. The digits stay the same, but their place value increases by a factor of 10.
- Take the decimal number (0.3)
- Move the decimal point one place to the right
- The result is 3.0 or simply 3
We have 0.3 as our decimal
When multiplying by 10, move the decimal point one place to the right
0.3 becomes 3.0 when the decimal moves one place right
3.0 is the same as 3
0.3 × 10 = 3
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Each digit's value increases by a factor of 10
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with tenths by 10: Moving the decimal point one place to the right converts tenths to ones.
We have 0.7 as our decimal
When multiplying by 10, move the decimal point one place to the right
0.7 becomes 7.0 when the decimal moves one place right
7.0 is the same as 7
0.7 × 10 = 7
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with ones and tenths by 10: Moving the decimal point one place to the right converts ones to tens and tenths to ones.
We have 1.4 as our decimal
When multiplying by 10, move the decimal point one place to the right
1.4 becomes 14.0 when the decimal moves one place right
14.0 is the same as 14
1.4 × 10 = 14
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Ones become tens, tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with tenths by 10: Moving the decimal point one place to the right converts tenths to ones.
We have 0.9 as our decimal
When multiplying by 10, move the decimal point one place to the right
0.9 becomes 9.0 when the decimal moves one place right
9.0 is the same as 9
0.9 × 10 = 9
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with ones and tenths by 10: Moving the decimal point one place to the right converts ones to tens and tenths to ones.
We have 2.5 as our decimal
When multiplying by 10, move the decimal point one place to the right
2.5 becomes 25.0 when the decimal moves one place right
25.0 is the same as 25
2.5 × 10 = 25
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Ones become tens, tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with tenths by 10: Moving the decimal point one place to the right converts tenths to ones.
We have 0.6 as our decimal
When multiplying by 10, move the decimal point one place to the right
0.6 becomes 6.0 when the decimal moves one place right
6.0 is the same as 6
0.6 × 10 = 6
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with ones and tenths by 10: Moving the decimal point one place to the right converts ones to tens and tenths to ones.
We have 3.8 as our decimal
When multiplying by 10, move the decimal point one place to the right
3.8 becomes 38.0 when the decimal moves one place right
38.0 is the same as 38
3.8 × 10 = 38
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Ones become tens, tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with tenths by 10: Moving the decimal point one place to the right converts tenths to ones.
We have 0.2 as our decimal
When multiplying by 10, move the decimal point one place to the right
0.2 becomes 2.0 when the decimal moves one place right
2.0 is the same as 2
0.2 × 10 = 2
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with ones and tenths by 10: Moving the decimal point one place to the right converts ones to tens and tenths to ones.
We have 4.7 as our decimal
When multiplying by 10, move the decimal point one place to the right
4.7 becomes 47.0 when the decimal moves one place right
47.0 is the same as 47
4.7 × 10 = 47
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Ones become tens, tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
Multiplying a decimal with tenths by 10: Moving the decimal point one place to the right converts tenths to ones.
We have 0.5 as our decimal
When multiplying by 10, move the decimal point one place to the right
0.5 becomes 5.0 when the decimal moves one place right
5.0 is the same as 5
0.5 × 10 = 5
• Decimal movement rule: Move decimal point one place right when multiplying by 10
• Place value: Tenths become ones
• Pattern recognition: Decimal point moves right for positive powers of 10
- Move the decimal point one place to the right
- If there's no visible decimal point, it's at the end of the number
- Each digit's place value increases by a factor of 10
- Moving right increases value (multiplication by 10)
- Moving left decreases value (division by 10)
- The number of places moved equals the exponent of 10
- Identify the decimal number to multiply
- Locate the decimal point (may be invisible at the end)
- Move the decimal point one place to the right
- Remove any trailing zeros after the decimal point
- The result is the answer
- 0.3 × 10 = 3.0 = 3 (decimal moves from .3 to 3.)
- 0.7 × 10 = 7.0 = 7 (decimal moves from .7 to 7.)
- 1.4 × 10 = 14.0 = 14 (decimal moves from 1.4 to 14.)
- 0.9 × 10 = 9.0 = 9 (decimal moves from .9 to 9.)
- Think of moving the decimal point, not the digits
- Remember: moving right multiplies, moving left divides
- Count the decimal places to verify your answer
- Check that the digits remain the same, only their place values change
- Moving the decimal point in the wrong direction
- Adding zeros instead of moving the decimal point
- Forgetting that the decimal point can be invisible at the end of whole numbers
- Changing the actual digits instead of just their place values
- "Multiply by 10, move decimal right"
- "Right for multiplication, left for division"
- Only the decimal point moves, not the digits
- Each move changes the place value by a factor of 10
- Decimals become whole numbers when the decimal point moves past them
Move the decimal point one place to the right
• Decimal point shows tenths
• 0.3 means 3 tenths
• 1.4 means 1 one and 4 tenths
• Decimal point moved right
• 3 tenths becomes 3 ones
• 14 tenths becomes 14 ones
| Multiplication | Rule Applied | Result |
|---|---|---|
| 0.3 × 10 | Move decimal right | 3 |
| 0.7 × 10 | Move decimal right | 7 |
| 1.4 × 10 | Move decimal right | 14 |
| 2.5 × 10 | Move decimal right | 25 |
| 0.6 × 10 | Move decimal right | 6 |
| 0.9 × 10 | Move decimal right | 9 |
| 3.8 × 10 | Move decimal right | 38 |
| 0.2 × 10 | Move decimal right | 2 |
Questions & Answers
Question: Why does multiplying by 10 move the decimal point to the right? It seems backwards!
Answer: It might seem backwards, but it makes sense when you think about place value! When you multiply by 10, you're making the number 10 times bigger.
For example, in 0.3, the 3 is in the tenths place. When you multiply by 10, that 3 becomes 10 times bigger, so it moves to the ones place (which is worth 10 times more).
Moving the decimal point to the right increases the value of each digit. Moving it to the left would make the number smaller, which would happen if you were dividing by 10.
Question: My child is struggling with the concept of decimal points. How can I help them understand?
Answer: Try using visual aids and real-world examples:
- Use money as an example: $0.25 is 25 cents, $2.50 is 2 dollars and 50 cents
- Show how the decimal point separates whole numbers from fractions
- Draw place value charts showing ones, tenths, hundredths
- Use base-10 blocks to represent decimals visually
The key is helping them see that the decimal point marks where whole units end and fractional parts begin.
Question: What happens if I multiply 0.05 by 10? Where does the decimal point go?
Answer: When you multiply 0.05 by 10, you move the decimal point one place to the right:
- Start with 0.05 (five hundredths)
- Move the decimal point one place right: 0.5 (five tenths)
So 0.05 × 10 = 0.5
The number becomes 10 times bigger, which makes sense: five hundredths becomes five tenths.