Arithmetic Operations
Dividing by Powers of 10
Dividing by a power of 10 is one of the fastest calculations you can do. Each division by 10 shifts every digit one place to the right through the place value columns.
Whole Numbers
| Calculation | Result |
|---|---|
| 540 ÷ 10 | 54 |
| 3,700 ÷ 100 | 37 |
| 85,000 ÷ 1,000 | 85 |
Decimals
Digits shift right. If the digit moves past the decimal point, a zero fills the vacant whole number place.
| Calculation | Result |
|---|---|
| 7.3 ÷ 10 | 0.73 |
| 4.56 ÷ 100 | 0.0456 |
| 0.5 ÷ 10 | 0.05 |
| 280 ÷ 1,000 | 0.28 |
General Rule
Count the zeros in the power of 10. Shift every digit that many places to the right.
45.6 ÷ 1,000: shift 3 right → 0.0456
Common Mistake
Do not "remove a zero" — this only works if there is a trailing zero. Say instead "shift digits right".
Key Takeaways
- Each ÷10 shifts digits one place right (making the number smaller).
- Insert leading zeros when needed to hold place value.
- The decimal point itself does not move — the digits do.
Practice: Shift the Digits
Divide by a Power of 10