Multiply by 10 using place value

Quick answer

When you multiply a number by 10, each digit moves one place to the left in the place value system. The digit that was in the ones place moves to the tens place, and so on. A zero is added to the ones place to fill the gap.

Learning outcome

By the end of this page, you will understand that multiplying by 10 means each digit moves one place value to the left, and you will be able to multiply any number by 10 using place value.

• You can explain how digits shift when multiplying by 10.
• You can multiply any number by 10 by moving digits one place to the left.
• You can show that multiplying by 10 is not just adding a zero.
• You can solve word problems involving multiplying by 10 using place value.

Why this matters

Understanding how place value works helps you solve bigger maths problems. When you multiply by 10, you're not just adding a zero – you're changing the value of each digit. This skill is useful when counting money, measuring things, or working out how many items you have in groups. It also helps you when you learn bigger multiplication tables later.

How it works

Let's think about how numbers work in place value. Each digit in a number has a special job. For example, in the number 234:

• The 4 is in the ones place
• The 3 is in the tens place
• The 2 is in the hundreds place

When you multiply by 10, each digit moves one place to the left:

1. The ones digit moves to the tens place
2. The tens digit moves to the hundreds place
3. The hundreds digit moves to the thousands place
4. A zero is added to the ones place to fill the gap

Examples you can see

Let's look at some examples using place value to multiply by 10.

You can also think of this like a journey. Imagine you're moving your toys:

• Each toy (digit) has a special place
• When you multiply by 10, you move each toy one step to the left
• There’s a new empty spot in the ones place
• You fill it with a zero

Try it as a mini adventure

Adventure: The Place Value Treasure Hunt

You are on a treasure hunt in a magical place where numbers are living creatures. Your mission is to find the secret of multiplying by 10. You have a number like 37. You must make it ten times bigger using place value magic.

1. Start with 37
2. Look at the 7 in the ones place
3. Move it to the tens place
4. Look at the 3 in the tens place
5. Move it to the hundreds place
6. Add a zero in the ones place
7. You now have 370!

Try this with other numbers like 52, 189, and 406. Can you find the pattern?

Common mistakes

• Mistake: Adding a zero to the end of any number to multiply by 10.
  Why it happens: This is a shortcut that works for some numbers but not all. It can confuse children.
  Fix: Remember, you're moving digits, not just adding zeros. Use place value to see how each digit changes.
• Mistake: Forgetting to add a zero in the ones place.
  Why it happens: Children might focus on moving the digits and forget the empty space.
  Fix: Always double-check that the ones place has a zero after multiplying by 10.
• Mistake: Thinking 10 × 10 = 100, but confusing it with 10 × 100 = 1000.
  Why it happens: Confusion with powers of ten.
  Fix: Use place value to show how digits shift for each multiplication by 10.

Parent and carer guide

Help your child understand multiplying by 10 using place value by:

1. Using physical objects like blocks or counters to show how digits shift
2. Creating a place value chart with columns for ones, tens, hundreds, etc.
3. Practising with numbers on a whiteboard or paper, moving digits with arrows
4. Using real-life examples like counting money or measuring things
5. Encouraging them to say out loud what happens to each digit

Don’t worry if they get it wrong at first – it's a new way of thinking about numbers. Be patient and keep practicing!

Practice questions

1. What is 8 × 10?
2. What is 42 × 10?
3. What is 156 × 10?
4. What is 309 × 10?
5. What is 700 × 10?

Answers:

1. 80
2. 420
3. 1560
4. 3090
5. 7000

FAQ

What happens when you multiply by 10?

Each digit moves one place to the left, and a zero is added in the ones place.

Why do we move digits instead of just adding a zero?

Moving digits shows the actual change in value. Adding a zero is just a trick that works for simple cases.

Can I use this method for any number?

Yes! This works for any number, including decimals and large numbers.

Is multiplying by 10 the same as dividing by 10?

No. Multiplying by 10 makes numbers bigger, while dividing by 10 makes them smaller.

How can I remember this rule?

Think of it like a dance: each digit steps one place to the left, and the ones place gets a zero to fill the gap.