Arithmetic Operations
Multiplying by Powers of 10
Multiplying by 10, 100, 1,000, or any power of 10 is one of the fastest calculations in maths — once you understand place value, it requires no written work at all.
Whole Numbers
Each multiplication by 10 shifts every digit one place to the left (equivalent to adding one zero).
| Calculation | Result |
|---|---|
| 37 × 10 | 370 |
| 37 × 100 | 3,700 |
| 37 × 1,000 | 37,000 |
| 37 × 10,000 | 370,000 |
Decimals
The decimal point stays fixed — the digits shift left. For each factor of 10, move each digit one place left.
| Calculation | Result |
|---|---|
| 4.56 × 10 | 45.6 |
| 4.56 × 100 | 456 |
| 0.07 × 1,000 | 70 |
| 2.3 × 10,000 | 23,000 |
Mixed Powers
250 × 40 = 250 × 4 × 10 = 1,000 × 10 = 10,000
Common Mistake
Students sometimes say "just add a zero" — this works for whole numbers but breaks for decimals. Say instead "shift digits one place left".
Key Takeaways
- Each ×10 shifts digits one place to the left.
- Count the zeros in the power of 10: that is how many places to shift.
- Works for decimals too — digits shift, not the decimal point.
Practice: Shift the Digits
Multiply by a Power of 10