Multiplying by 10, 100, and 1,000- Quick Techniques
Why Multiplying by 10, 100, and 1,000 Matters
You don't need a calculator for this. Multiplying by powers of 10 is the easiest mental math you can learn. Once you see the pattern, you'll never reach for your phone to solve 47 × 100.
These skills save time at the store, at work, and anywhere numbers appear. Here's how to do it fast.
The Core Rule: Just Add Zeros
When you multiply any whole number by 10, you add one zero to the end. That's it.
Multiplying by 100? Add two zeros. Multiplying by 1,000? Three zeros.
This works because our number system is base-10. Each place value is ten times bigger than the one before it. Moving left in a number multiplies by 10. Simple.
Examples
- 7 × 10 = 70
- 7 × 100 = 700
- 7 × 1,000 = 7,000
- 45 × 10 = 450
- 45 × 100 = 4,500
- 45 × 1,000 = 45,000
What About Numbers That Already Have Zeros?
Same rule applies. Look at the number, count the zeros, add yours.
200 × 100 = 20,000
You're not "adding zeros to zeros." You're just attaching the total zeros together. 200 has two zeros. 100 has two zeros. Together that's four zeros on 2, giving you 20,000.
Decimals Change the Rules
Here's where people get confused. When multiplying decimals by 10, 100, or 1,000, you move the decimal point, not add zeros.
3.5 × 10 = 35
Move the decimal one place right. The decimal in 3.5 is between the 3 and the 5. Slide it right: 35.
3.5 × 100 = 350
Move it two places right. 3.5 → 35 → 350.
3.5 × 1,000 = 3,500
Three places right. 3.5 → 35 → 350 → 3,500.
If you run out of numbers to move past, add zeros as placeholders.
2.4 × 1,000 = 2,400
Quick Comparison Table
| Problem | Method | Answer |
|---|---|---|
| 8 × 10 | Add 1 zero | 80 |
| 8 × 100 | Add 2 zeros | 800 |
| 8 × 1,000 | Add 3 zeros | 8,000 |
| 12 × 10 | Add 1 zero | 120 |
| 12 × 100 | Add 2 zeros | 1,200 |
| 12 × 1,000 | Add 3 zeros | 12,000 |
| 4.7 × 10 | Move decimal 1 place right | 47 |
| 4.7 × 100 | Move decimal 2 places right | 470 |
| 4.7 × 1,000 | Move decimal 3 places right | 4,700 |
Common Mistakes
- Adding zeros to decimals — 5.3 × 100 is NOT 5.300. It's 530. Move the decimal, don't add zeros.
- Forgetting trailing zeros on whole numbers — 56 × 100 needs two zeros: 5,600. People sometimes write 56 and forget to attach the zeros.
- Moving the decimal the wrong direction — Multiplying always moves the decimal right. Dividing moves it left.
How to Practice
Grab a pack of index cards. Write problems on one side, answers on the other. Spend five minutes a day.
Or do this: look at prices when shopping. That $4.50 item times 10 is $45. Does that math check out in your head? Train yourself to notice numbers around you.
Another method: say the problem aloud and give the answer immediately. "Thirty-seven times one hundred. Three thousand seven hundred." Speed builds retention.
When to Use Mental Math vs a Calculator
For problems like 47 × 100, mental math wins every time. It's faster than opening an app.
Use a calculator when you're dealing with decimals that don't land on clean numbers, or when the problem involves larger multipliers like 10,000 or 100,000. At that point, precision matters more than speed.
But for 10, 100, and 1,000? Your brain is the tool. No app needed.