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.
Multiplying by 10, 100, or 1,000 changes the place value of the digits.
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
"Just Add Zeros" Trap!
"Add a zero at the end" works for whole numbers, but not with decimals:
- The Trap: 4.5 × 10 becomes 4.50 (The value didn't change at all!)
- The Correct Way: 4.5 × 10 = 45 (The digits shifted left)
It is always safer and more accurate to think of the digits shifting.
Mental Math
When one number is a multiple of 10, 100, or 1,000, we can use a simple strategy:
Multiply the digits first, then multiply by 10, 100, or 1,000.
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.
- 9 × 1,000 = 9,000
- 7 × 40
7 × 4 = 28 → 280 - 5 × 600
5 × 6 = 30, then 30 × 100 = 3,000
(Notice how 30 already has a zero, and we still shift it two more places!)
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
Activity: Shift the Digits
Start with a basic fact:
6 × 3 = 18
Now try:
- 6 × 30 = ______
- 6 × 300 = ________
- 6 × 3,000 = __________
What stayed the same? What changed?
26529, 26530, 26531, 26532, 26533, 26534, 26535, 26536, 26537, 26538