The number system
Multiplying & dividing by 10, 100 and 1000
When you multiply or divide by 10, 100 or 1000, the digits move places while the decimal point stays still.
Which way do the digits move?
• Multiplying makes a number BIGGER, so the digits move to the LEFT. • Dividing makes a number SMALLER, so the digits move to the RIGHT. Move 1 place for 10, 2 places for 100, and 3 places for 1000.
Worked examples
Multiplying: 3.45 × 100
- Multiplying by 100 makes the number bigger, so the digits move two places to the LEFT.
- 3.45 becomes 345.
Answer: 3.45 × 100 = 345
Dividing: 16.8 ÷ 10
- Dividing by 10 makes the number smaller, so the digits move one place to the RIGHT.
- 16.8 becomes 1.68.
Answer: 16.8 ÷ 10 = 1.68
Where you see this in real life
- Changing between centimetres and metres (÷ 100).
- Working out the cost of 100 identical items (× 100).
- Changing grams to kilograms (÷ 1000).
Key words
- Digit
- One of the symbols 0–9 used to write numbers.
- Place value
- The value of a digit because of its position in the number.
- Decimal point
- The dot that separates whole numbers from parts of a number.