Case 1: Dividing a decimal by a whole number
Divide as usual and put the decimal point in the quotient directly above the decimal point in the dividend.
Example: 7.2 ÷ 3
- 3 into 7 → 2 R1
- Decimal point goes up
- 3 into 12 → 4
- Quotient: 2.4
Case 2: Dividing by a decimal
Turn the divisor into a whole number by multiplying both numbers by the same power of 10. This makes an equivalent division with the same answer.
Example: 4.5 ÷ 0.15
- Multiply both by 100: 450 ÷ 15
- 450 ÷ 15 = 30
Why it works: 4.5/0.15 = 450/15, just like 1/2 = 100/200.
Example: 2.4 ÷ 0.6 → × 10 → 24 ÷ 6 = 4
Case 3: Continuing past the dividend
If there’s a remainder, annex zeros to keep dividing.
Example: 3 ÷ 8
- 3.000 ÷ 8: 8 into 30 → 3 R6; into 60 → 7 R4; into 40 → 5
- Quotient: 0.375
Some divisions never end: 1 ÷ 3 = 0.333… (round as needed).
Dividing by powers of 10
Dividing by 10, 100 or 1,000 moves the decimal point left 1, 2 or 3 places.
| Number | ÷ 10 | ÷ 100 | ÷ 1,000 |
|---|---|---|---|
| 456 | 45.6 | 4.56 | 0.456 |
| 7.2 | 0.72 | 0.072 | 0.0072 |
Bigger or smaller?
Dividing by a decimal less than 1 makes the answer bigger: 5 ÷ 0.5 = 10. (How many halves fit into 5? Ten.)
Estimate to check
- 19.6 ÷ 4.1 ≈ 20 ÷ 4 = 5. Exact ≈ 4.78 ✓
- 0.84 ÷ 0.2 ≈ 0.8 ÷ 0.2 = 4. Exact = 4.2 ✓
Real-life division
- Unit price: 6 cans cost $8.94. Each can: 8.94 ÷ 6 = $1.49.
- Pieces: How many 0.25 m pieces from 3 m of wire? 3 ÷ 0.25 = 12.
- Fuel: 42.5 L used over 500 km → 42.5 ÷ 5 = 8.5 L per 100 km.
Worked examples
Example 1: 9.36 ÷ 4
4 into 9 → 2 R1; 13 → 3 R1; 16 → 4 → 2.34.
Example 2: 1.8 ÷ 0.03
× 100 → 180 ÷ 3 = 60.
Example 3: 5 ÷ 4
5.00 ÷ 4 = 1.25.
Common mistakes
- Multiplying only the divisor by 10 or 100 and not the dividend.
- Misplacing the decimal point in the quotient.
- Stopping at a remainder instead of annexing zeros.
Try it yourself
- 8.4 ÷ 4
- 6.3 ÷ 0.7
- 0.48 ÷ 0.012
- 7 ÷ 20
- A 2.5 kg bag of rice is split into 0.125 kg portions. How many portions?
Answers: 1) 2.1 2) 9 3) 40 4) 0.35 5) 20
Quick recap
- Dividing by a whole number: line the quotient’s point up with the dividend’s.
- Dividing by a decimal: multiply both by a power of 10 first.
- Annex zeros to continue; estimate to check.