Dividing Decimals
What Is This?
Dividing decimals means splitting a decimal number into equal parts — or finding out how many times one decimal fits into another. There are two main situations you will encounter: dividing a decimal by a whole number, and dividing a decimal by another decimal. Each has a clear method, and both build directly on long division skills you already know.
Why Does It Matter?
Dividing decimals appears everywhere in real life: splitting a bill, calculating a unit price, finding how many equal lengths fit into a measurement, and converting rates. It also underpins percentage calculations and algebraic reasoning at higher grades.
Method 1 — Dividing a Decimal by a Whole Number
The key idea: keep the decimal point in the same position and divide exactly as you would with whole numbers.
Example: 8.4 ÷ 4
Step 1: Set up as long division. Place the decimal point in the answer directly above the decimal point in the dividend.
_ . _
4 ) 8 . 4
Step 2: Divide normally.
- 8 ÷ 4 = 2 (ones)
- 4 ÷ 4 = 1 (tenths)
2 . 1
4 ) 8 . 4
Answer: 2.1 ✓
Example: 7.35 ÷ 3
2 . 4 5
3 ) 7 . 3 5
- 7 ÷ 3 = 2 remainder 1
- 13 ÷ 3 = 4 remainder 1
- 15 ÷ 3 = 5
Answer: 2.45 ✓
Method 2 — Dividing a Decimal by a Decimal
The key idea: convert the divisor to a whole number first by multiplying both the dividend and divisor by the same power of 10. This does not change the answer — it just makes the division easier.
Example: 6.4 ÷ 0.8
Step 1: The divisor (0.8) has 1 decimal place. Multiply both numbers by 10.
- 6.4 × 10 = 64
- 0.8 × 10 = 8
Step 2: Now divide whole numbers.
- 64 ÷ 8 = 8
Answer: 8 ✓
Example: 3.75 ÷ 0.25
Step 1: The divisor (0.25) has 2 decimal places. Multiply both by 100.
- 3.75 × 100 = 375
- 0.25 × 100 = 25
Step 2: Divide.
- 375 ÷ 25 = 15
Answer: 15 ✓
What Power of 10 to Use?
| Divisor | Decimal places | Multiply both by |
|---|---|---|
| 0.4 | 1 | 10 |
| 0.07 | 2 | 100 |
| 0.005 | 3 | 1000 |
Always look at the divisor — the number you are dividing by — and count its decimal places.
Adding Zeros to the Dividend
Sometimes the dividend doesn't divide evenly. You can add a zero to the right of the last decimal digit and keep dividing.
Example: 5 ÷ 4
1 . 2 5
4 ) 5 . 0 0
- 5 ÷ 4 = 1 remainder 1
- 10 ÷ 4 = 2 remainder 2
- 20 ÷ 4 = 5
Answer: 1.25 ✓
Worked Examples
Worked Example 1: 9.6 ÷ 6
1 . 6
6 ) 9 . 6
- 9 ÷ 6 = 1 remainder 3
- 36 ÷ 6 = 6 (bring down the 6 in tenths)
Wait — note the correct reading: after getting remainder 3 in the ones, bring down the 6 (tenths digit). So 36 ÷ 6 = 6. Place the 6 in the tenths position.
Answer: 1.6 ✓
Worked Example 2: 14.4 ÷ 0.6
Multiply both by 10: 144 ÷ 6 = 24
Worked Example 3: 2.8 ÷ 0.04
Multiply both by 100: 280 ÷ 4 = 70
Worked Example 4: 0.36 ÷ 4
0 . 0 9
4 ) 0 . 3 6
- 0 ÷ 4 = 0 (ones)
- 3 ÷ 4 = 0 remainder 3 (tenths — write 0, carry 3)
- 36 ÷ 4 = 9 (hundredths)
Answer: 0.09 ✓
Worked Example 5 (Word Problem): A piece of rope is 4.5 m long. It is cut into pieces each 0.9 m long. How many pieces are there?
4.5 ÷ 0.9 → multiply both by 10 → 45 ÷ 9 = 5 pieces
Checking Your Answer
Multiply the answer by the divisor — you should get the dividend back.
- 2.1 × 4 = 8.4 ✓
- 8 × 0.8 = 6.4 ✓
- 15 × 0.25 = 3.75 ✓
Estimating to Check
Round to the nearest whole number (or friendly decimal) before dividing.
Example: 9.6 ÷ 3.2
- Estimate: 10 ÷ 3 ≈ 3
- Exact: 96 ÷ 32 = 3 ✓
Common Mistakes
Mistake 1: Moving the decimal point in the dividend only When dividing a decimal by a decimal, you MUST multiply both numbers by the same power of 10 — not just the divisor. 6.4 ÷ 0.8: multiply both by 10 → 64 ÷ 8. If you only change 0.8 to 8, you get a different (wrong) division.
Mistake 2: Forgetting to place the decimal point in the answer When dividing a decimal by a whole number, the decimal point in the answer must sit directly above the decimal point in the dividend. Forgetting it gives an answer that is 10 or 100 times too large.
Mistake 3: Not adding zeros when the division doesn't end evenly 5 ÷ 4 doesn't end at 1 remainder 1 — you can add a decimal point and zeros (5.00) and keep going to get 1.25.
Mistake 4: Confusing which number is the divisor In 6.4 ÷ 0.8, the divisor is 0.8 — the number after the ÷ sign. Always check your divisor's decimal places before deciding how much to multiply.
Key Takeaways
- To divide a decimal by a whole number: place the decimal point in the answer directly above the decimal point in the dividend, then divide normally
- To divide a decimal by a decimal: multiply both numbers by 10, 100, or 1000 to make the divisor a whole number, then divide
- The number of places to shift depends on the decimal places in the divisor
- You can always add zeros to the dividend and continue dividing if the answer isn't exact
- Check your answer by multiplying it back by the divisor
Practice and Resources
Ready to practise? Try our Grade 3-5 Dividing Decimals Worksheet covering decimal ÷ whole number, decimal ÷ decimal, and word problems. Test yourself with the Grade 3-5 Math Practice Test.