Multiplying by 10, 100, and 1,000

Look at the pattern:

• 5 × 1 = 5
• 5 × 10 = 50
• 5 × 100 = 500
• 5 × 1,000 = 5,000

The digit stays the same, but its value moves left each time.

The key idea is place value.

Think in groups:

• 4 × 10 means 4 tens = 40
• 3 × 100 means 3 hundreds = 300
• 2 × 1,000 means 2 thousands = 2,000

Move It Along

Every time we multiply by 10 we move the digits along 1 place:

3

× 10

30

× 10

300

× 10

3,000

Multiplying by 100 moves the digits along 2 places:

3

× 100

300

× 100

30,000

Multiplying by 1,000 moves the digits along 3 places:

3

× 1,000

3,000

Mental Math Strategies

When one number is a multiple of 10, 100, or 1,000, we can use a simple strategy:

Examples:

• 4 × 30
  4 × 3 = 12, then 12 × 10 = 120
• 6 × 400
  6 × 4 = 24, then 24 × 100 = 2,400
• 3 × 2,000
  3 × 2 = 6, then 6 × 1,000 = 6,000

After some practice we can do many of these in our head.

• 7 × 40
  7 × 4 = 28 → 280
• 9 × 1,000 = 9,000
• 5 × 600
  Half of 6,000 is 3,000

Real-Life Examples

Multiplying multiples of 10, 100, and 1,000 is very useful in real life.

• Each box holds 20 pencils. 6 boxes hold 6 × 20 = 120 pencils
• A team earns 100 points each game. After 7 games they have 700 points
• A school orders 3 packs of 1,000 stickers. That's 3,000 stickers