Multiplying decimals by 10
Use place value to make a number ten times larger.
Quick answer
When you multiply a decimal by 10, you move the decimal point one place to the right. The number becomes ten times larger.
Learning outcome
By the end of this page, you will be able to multiply decimals by 10 and understand how the decimal point moves to make the number ten times bigger.
- You can move the decimal point one place to the right when multiplying by 10.
- You understand that multiplying by 10 makes a number ten times bigger.
- You can use place value to explain why the decimal point moves.
- You can solve real-life problems involving multiplying decimals by 10.
Why this matters
Multiplying decimals by 10 is a useful skill in everyday life. You might need it when:
- Shopping and working out prices for 10 items
- Measuring ingredients for a recipe that needs to be made 10 times bigger
- Working out how far you can travel in 10 minutes if you know your speed
- Calculating how much money you would have if you had 10 times your current amount
Learning this helps you understand how numbers change and gives you a solid foundation for working with bigger numbers and decimals later on.
How it works
Let's look at how multiplying decimals by 10 works step by step:
- Look at the decimal number you have
- Find the decimal point (the dot)
- Move the decimal point one place to the right
- Fill in any empty spaces with zeros if needed
- That's your new number, ten times bigger!
It's like taking a number and giving it ten times the value!
Examples you can see
Let's work through some examples to see how this works:
| Original Number | Decimal Point Moves | New Number |
|---|---|---|
| 2.5 | 2.5 → 25. | 25 |
| 0.78 | 0.78 → 7.8 | 7.8 |
| 3.14 | 3.14 → 31.4 | 31.4 |
| 0.05 | 0.05 → 0.5 | 0.5 |
| 12.345 | 12.345 → 123.45 | 123.45 |
Notice how we moved the decimal point one place to the right. When there isn't a digit to move the decimal point past, we just add a zero at the end!
Try it as a mini adventure
Adventure: The Treasure Hunt
You are on a treasure hunt! You have found a map with clues that tell you how far to walk. Each clue is a decimal number, and you need to multiply it by 10 to find the next location.
Your first clue says: "Walk 0.6 km".
Where do you go next?
- Original clue: 0.6 km
- Move decimal point one place right: 6.0 km
- Next location: 6 km
Your second clue says: "Dig 1.23 m from the big tree".
How far do you dig?
- Original clue: 1.23 m
- Move decimal point one place right: 12.3 m
- Dig at: 12.3 m
Your final clue says: "Look for the treasure 0.04 km from the old bridge".
How far is that?
- Original clue: 0.04 km
- Move decimal point one place right: 0.4 km
- Look for treasure at: 0.4 km
You've solved the treasure hunt using multiplication by 10!
Common mistakes
- Mistake: Moving the decimal point to the left instead of the right
Why it happens: Confusing the direction of movement
Fix: Remember: multiplying by 10 makes the number bigger, so move the decimal point to the right - Mistake: Not adding zeros when needed
Why it happens: Thinking the decimal point just disappears
Fix: When you move the decimal point and there's an empty space, fill it with a zero - Mistake: Moving the decimal point more than one place
Why it happens: Getting excited about the math
Fix: Count carefully and only move one place to the right - Mistake: Forgetting that whole numbers still have decimal points
Why it happens: Not thinking about place value
Fix: Remember that 5 is the same as 5.0, and 25 is the same as 25.0
Parent and carer guide
Helping your child understand multiplying decimals by 10 is all about place value and making it visual:
- Use everyday objects: Count out 3.5 coins and show how 10 times that is 35 coins
- Draw it: Draw a decimal point and move it with a finger or marker to show the change
- Make it fun: Play the treasure hunt game together to practice
- Ask questions: "Why did we move the decimal point?" or "What happens to the value?"
- Watch for: Confusion about moving the decimal point in the wrong direction
- Remember: It's okay if they make mistakes – they're learning!
Try to make this a conversation, not a test. Let your child explain how they think about it.
Practice questions
- What is 4.2 × 10?
Answer: 42 - What is 0.8 × 10?
Answer: 8 - What is 1.56 × 10?
Answer: 15.6 - What is 0.07 × 10?
Answer: 0.7 - What is 23.45 × 10?
Answer: 234.5 - What is 0.345 × 10?
Answer: 3.45 - What is 7.0 × 10?
Answer: 70 - What is 0.009 × 10?
Answer: 0.09
FAQ
Why does the decimal point move when multiplying by 10?
When you multiply by 10, each digit's place value increases by one place. The decimal point doesn't actually move – it's the digits that shift to the left, making the number ten times bigger.
Can I multiply any decimal by 10?
Yes! Any decimal number can be multiplied by 10. You just move the decimal point one place to the right.
What if there are no digits after the decimal point?
If there are no digits after the decimal point, like in 5.0, you still move the decimal point one place to the right, which makes it 50.
Is multiplying by 10 the same as dividing by 0.1?
Yes! Multiplying by 10 is the same as dividing by 0.1. Both make a number ten times bigger.
How can I check if my answer is right?
Divide your answer by 10. If you get back to the original number, your answer is correct!