Long division with whole numbers is hard enough to remember from school. Add a decimal point to the divisor or the dividend and many people freeze. The good news is that decimal division isn't a new method at all. It's the same long division you already know, with one preparation step and one rule for placing the point. This guide walks through both, with worked examples.
The key idea: make the divisor a whole number
Dividing by a decimal is awkward, but multiplying both numbers by the same power of ten doesn't change the answer. For example:
2.4 ÷ 0.6 = 24 ÷ 6 = 4
Both numbers were multiplied by 10. The quotient stays the same because a division is really a fraction, and multiplying the top and bottom of a fraction by the same number leaves its value unchanged.
So the first step is always:
- Count the decimal places in the divisor.
- Move the decimal point that many places to the right in both the divisor and the dividend, adding zeros to the dividend if needed.
Case 1: Decimal in the dividend only
Example: 7.56 ÷ 4
The divisor is already whole, so divide as usual and put the decimal point in the answer directly above the point in the dividend.
- 4 into 7 goes 1, remainder 3.
- Bring down 5: 4 into 35 goes 8, remainder 3.
- Place the decimal point in the answer.
- Bring down 6: 4 into 36 goes 9, remainder 0.
Answer: 1.89
Case 2: Decimal in the divisor
Example: 9.1 ÷ 0.35
The divisor has two decimal places, so move both points two places right:
- 0.35 becomes 35
- 9.1 becomes 910 (adding one zero)
Now divide 910 by 35:
- 35 into 91 goes 2 (70), remainder 21.
- Bring down 0: 35 into 210 goes 6 exactly.
Answer: 26
Check: 26 × 0.35 = 9.1. ✓
Case 3: The division doesn't come out evenly
Example: 5 ÷ 0.8
Move one place: 50 ÷ 8.
- 8 into 50 goes 6 (48), remainder 2.
- Add a decimal point and a zero: 20. 8 into 20 goes 2 (16), remainder 4.
- Bring down another zero: 40. 8 into 40 goes 5, remainder 0.
Answer: 6.25
You can keep adding zeros after the decimal point for as long as you need. The dividend 50 is the same as 50.000…
Case 4: Repeating decimals
Some divisions never end. Example: 2 ÷ 0.3
Move one place: 20 ÷ 3.
- 3 into 20 goes 6, remainder 2.
- Add a point and a zero: 20 again. 3 into 20 goes 6, remainder 2…
The remainder repeats, so the digit repeats forever: 6.666…, written 6.6̅ with a bar over the repeating 6, or rounded to a sensible number of places such as 6.67.
Whenever you see a remainder you've had before, you've found the start of a repeating pattern.
Estimating first
Before dividing, estimate. For 9.1 ÷ 0.35, think: 0.35 is about a third, and dividing by a third is like multiplying by 3, so the answer should be a bit under 9 × 3 = 27. Getting 26 matches. If you'd got 2.6 or 260, you'd know the decimal point was in the wrong place.
Common mistakes
- Moving the point in the divisor but not the dividend. Both must move the same number of places.
- Forgetting to add zeros when the dividend runs out of digits.
- Misplacing the point in the answer. Line it up directly above the (moved) point in the dividend.
- Stopping too early. Decide how many decimal places you need, then work one place further so you can round correctly.
Checking your answer
Multiply the quotient by the original divisor. You should get the original dividend (or very close, if you rounded). This check catches almost every decimal-point error.
If you want to compare your written working against a full worked solution, this step-by-step decimal divider shows each subtraction and bring-down, including where repeating digits begin.
Summary
To divide decimals: make the divisor whole by moving both decimal points the same number of places, divide as normal, keep the point aligned in the answer and add zeros as needed. Estimate first, check by multiplying afterwards, and look out for repeating remainders.