Why multiplying by ten is place value

Quick answer

Multiplying by ten moves each digit one place to the left, and a zero is added in the ones place. This is how place value works, not just "adding a zero".

Learning outcome

By the end of this page, you will understand that multiplying by ten shifts digits one place left, and that this is how place value works, not just adding a zero.

• You can explain how multiplying by ten changes the value of each digit
• You can show how tens and ones move when multiplying by ten
• You can solve problems using place value when multiplying by ten
• You can explain why "adding a zero" is not the full story

Why this matters

Understanding how multiplying by ten works helps you with bigger maths like decimals, money, and measurements. It also helps you understand how numbers grow when you multiply. When you know this, you'll be ready for bigger numbers and more complex maths later on. It's like learning the secret code of numbers!

How it works

When you multiply by ten, every digit moves one place to the left. This is because each place is worth ten times the place to its right.

1. Start with any number like 42
2. Look at each digit's place value: 4 is in the tens place, 2 is in the ones place
3. Multiply by ten: 42 × 10 = 420
4. Each digit moves one place to the left: 4 moves from tens to hundreds, 2 moves from ones to tens
5. Zero is added in the ones place to fill the gap

This is how place value works. It's not just "adding a zero" – it's moving digits!

Examples you can see

Let's look at how this works with different numbers:

Try this with your fingers or draw it out. You can use blocks or counters to show how the digits move.

Try it as a mini adventure

Adventure: The Place Value Treasure Hunt

You are a treasure hunter and need to find a hidden treasure. The map shows you must go to the place where the number 23 is multiplied by ten to find the treasure.

First, you see the number 23. You know 2 is in the tens place and 3 is in the ones place.

Then you multiply by ten. What do you get?

1. 2 moves from tens to hundreds
2. 3 moves from ones to tens
3. A zero is added in the ones place
4. You get 230

So the treasure is at 230! This is how place value helps you find the answer.

Common mistakes

• Mistake: Thinking that multiplying by ten just means adding a zero at the end.
  Why it happens: This is a shortcut that works for whole numbers but not for decimals or fractions.
  Fix: Remember that each digit moves one place to the left and a zero is added in the ones place.
• Mistake: Forgetting that the zero in the ones place is needed to keep the number's value.
  Why it happens: Kids often think the zero is extra or not needed.
  Fix: Practice with counters or drawings to see how the place value changes.
• Mistake: Thinking that multiplying by ten makes numbers smaller.
  Why it happens: This confusion happens because the digits move to a higher place value.
  Fix: Remember that each digit's value increases by ten times, so the whole number gets bigger.

Parent and carer guide

Help your child understand place value by using everyday examples:

• Use base ten blocks or counters to show how digits move
• Practice with numbers like 4, 40, 400 to see the pattern
• Ask questions like: "What happens to the 4 in 42 when we multiply by ten?"
• Encourage drawing the place value chart to see the movement
• Use real-life situations like counting money or measuring ingredients

Remember: This is about understanding the pattern, not just memorising the rule. Keep it fun and visual!

Practice questions

1. What is 7 × 10?
2. What is 56 × 10?
3. What is 304 × 10?
4. What is 123 × 10?
5. What is 9 × 10?

Answers:

1. 70
2. 560
3. 3040
4. 1230
5. 90

FAQ

Why does multiplying by ten move digits?

Because place value works in tens. Each place is worth ten times the place to its right. So when you multiply by ten, you're shifting each digit to the next higher place.

Does this work with decimals?

Yes! When you multiply 0.5 by ten, it becomes 5.0. The 5 moves from tenths to ones, and the zero is added in the tenths place.

What if I have a number with zeros?

It still works the same way. For example, 20 × 10 = 200. The 2 moves from tens to hundreds, and 0 is added in the ones place.

Can I use this with bigger numbers?

Absolutely! This works with any number, no matter how big. For example, 1234 × 10 = 12340. Each digit moves one place left.

Why can't I just add a zero?

Adding a zero only works for whole numbers. For decimals, you need to move the digits to show the correct place value. For example, 3.4 × 10 = 34, not 3.40.

Times table facts: 10 times table