X Tables
Place Value

Multiply and divide by 100

Use charts and sliders to explain two-place shifts.

Quick answer

When you multiply a number by 100, you move each digit two places to the left. When you divide a number by 100, you move each digit two places to the right.

Learning outcome

By the end of this page, you will understand how multiplying and dividing by 100 changes the place value of each digit in a number. Success signs:
  • You can explain why multiplying by 100 makes a number bigger
  • You can show how digits move when you multiply or divide by 100
  • You can solve simple multiplication and division problems with 100
  • You can use place value charts to help you work out the answers

Why this matters

Multiplying and dividing by 100 helps you understand how numbers work. You use this in real life when you:
  • Measure things in metres and centimetres
  • Count money in pounds and pence
  • Work out how much you spend or save
  • Play games that involve scores or points
When you understand place value, you can do bigger maths problems more easily. It's like having a secret code that helps you move numbers around!

How it works

Think of place value like a row of houses. Each house has a number, and each number has a special job:
  • The ones house (rightmost) is worth 1
  • The tens house is worth 10
  • The hundreds house is worth 100
  • The thousands house is worth 1,000
When you multiply by 100, you move each house two places to the left. When you divide by 100, you move each house two places to the right. Let's look at this step by step:
  1. Start with any number, like 45
  2. Write it in a place value chart
  3. Multiply by 100: move each digit two places left
  4. Divide by 100: move each digit two places right

Examples you can see

Let's start with a simple example: 63 Step 1: Write it in a place value chart
HundredsTensOnes
063
Step 2: Multiply by 100 When we multiply by 100, we move each digit two places to the left:
HundredsTensOnes
630
So 63 × 100 = 6,300 Step 3: Divide by 100 When we divide by 100, we move each digit two places to the right:
HundredsTensOnes
0063
So 63 ÷ 100 = 0.63 Here are more examples:
Number× 100÷ 100
272,7000.27
15415,4001.54
88000.08
30030,0003

Try it as a mini adventure

Adventure: The Magic Shop You are the shopkeeper of a magical store where everything costs 100 times more than normal! You have 12 items:
  • 1 pencil = 10p
  • 1 ruler = 20p
  • 1 eraser = 5p
  • 1 pen = 15p
  • 1 notebook = 25p
  • 1 highlighter = 8p
  • 1 sharpener = 12p
  • 1 calculator = 30p
  • 1 compass = 18p
  • 1 protractor = 22p
  • 1 set of coloured pencils = 35p
  • 1 geometry kit = 45p
In your magic shop, everything costs 100 times more:
  • 1 pencil = 10p × 100 = 1,000p = £10
  • 1 ruler = 20p × 100 = 2,000p = £20
  • 1 eraser = 5p × 100 = 500p = £5
Challenge: What would 12 pencils cost in your magic shop? Answer: 12 × 100 = 1,200p = £12 Another challenge: If you had £30, how many erasers could you buy in the magic shop? Answer: £30 = 3,000p. Each eraser costs 500p. 3,000 ÷ 500 = 6 erasers

Common mistakes

  • Mistake: Thinking 45 × 100 = 450
    Why it happens: Confusing with multiplying by 10 instead of 100
    Fix: Remember that × 100 means moving two places, not one
  • Mistake: Thinking 700 ÷ 100 = 70
    Why it happens: Thinking you're dividing by 10 instead of 100
    Fix: Remember that ÷ 100 means moving two places, not one
  • Mistake: Forgetting to add zeros when multiplying by 100
    Why it happens: Not understanding place value shifts
    Fix: Use a place value chart to see where digits go
  • Mistake: Thinking 0.5 × 100 = 5
    Why it happens: Confusing decimal and whole number place value
    Fix: 0.5 = 5 tenths. When we multiply by 100, we get 500 hundredths = 5

Parent and carer guide

You can help your child understand multiplying and dividing by 100 by:
  • Using a place value chart together
  • Playing the magic shop game
  • Looking at real money amounts
  • Using everyday examples like measuring
What to say:
  • "Let's see where each digit goes when we multiply by 100"
  • "Think of it like moving houses - each digit gets a new home two places away"
  • "What happens when we divide by 100?"
What not to worry about:
  • Children might make mistakes at first - that's normal
  • They don't need to memorize every fact right away
  • Using visual aids like charts helps them understand
Quick practice tip: Ask your child to multiply 24 by 100 and then divide 2,400 by 100. Check if they moved the digits the right number of places.

Practice questions

  1. What is 34 × 100?
  2. What is 870 ÷ 100?
  3. What is 5 × 100?
  4. What is 6,000 ÷ 100?
  5. What is 123 × 100?
  6. What is 1,230 ÷ 100?
  7. What is 70 × 100?
  8. What is 9,000 ÷ 100?
  9. What is 200 × 100?
  10. What is 3,500 ÷ 100?
Answers:
  1. 3,400
  2. 8.7
  3. 500
  4. 60
  5. 12,300
  6. 12.3
  7. 7,000
  8. 90
  9. 20,000
  10. 35

FAQ

Why does multiplying by 100 move digits two places?

Because 100 = 10 × 10, and each multiplication by 10 moves digits one place. So 100 moves them two places.

Can I use this with decimal numbers?

Yes! For example, 0.4 × 100 = 40. The decimal point moves two places to the right.

How can I remember which way to move digits?

Remember: Multiply = move left. Divide = move right. And always move two places for 100.

What if I have a number with zeros?

That's fine! For example, 200 × 100 = 20,000. The zeros stay but the other digits move.

Is this the same as multiplying by 10 twice?

Yes! 10 × 10 = 100, so multiplying by 100 is the same as multiplying by 10 twice.