How to divide decimals
Long division with decimals is ordinary long division with two extra rules. One is about the number you divide by, and one is about where the point goes in the answer.
The divisor has to be a whole number: if it is not, move the decimal point in both numbers the same number of places. Then divide as usual, and put the point in the answer straight above the point in the dividend.
How to do it
- If the divisor has a decimal point, move it to the end so the divisor is a whole number. Move the dividend's decimal point the same number of places, writing zeros on the end if you run out of digits.
- Set out the long division as usual.
- Divide as for whole numbers. When you bring down the first digit after the decimal point, the decimal point goes into the answer, straight above the one in the dividend.
- If the remainder is not 0 when the digits run out, add a 0 after the decimal point and bring it down. Keep going until nothing is left.
Worked examples
What is 12.6 ÷ 3?
| 4. | 2 | ||
| 3 | 1 | 2. | 6 |
| − | 1 | 2 | |
| 6 | |||
| − | 6 | ||
| 0 |
12 ÷ 3 = 4. The next digit down is the 6 after the point, so the point goes into the answer before 6 ÷ 3 = 2. 12.6 ÷ 3 = 4.2.
What is 2.4 ÷ 6?
| 0. | 4 | |
| 6 | 2. | 4 |
| − | 2 | 4 |
| 0 |
6 does not go into 2, so the answer starts 0. Then the 4 comes down, the point goes in, and 24 ÷ 6 = 4. 2.4 ÷ 6 = 0.4.
What is 127 ÷ 4, as a decimal?
127 ÷ 4 leaves 3 over, so write 127 as 127.00 and keep going.
| 3 | 1. | 7 | 5 | ||
| 4 | 1 | 2 | 7. | 0 | 0 |
| − | 1 | 2 | |||
| 7 | |||||
| − | 4 | ||||
| 3 | 0 | ||||
| − | 2 | 8 | |||
| 2 | 0 | ||||
| − | 2 | 0 | |||
| 0 |
The 3 left over becomes 30 tenths, then the 2 left after that becomes 20 hundredths, and the division comes out. 127 ÷ 4 = 31.75.
What is 1.68 ÷ 0.4?
The divisor has to be a whole number, so move both points one place. 1.68 ÷ 0.4 = 16.8 ÷ 4
| 4. | 2 | ||
| 4 | 1 | 6. | 8 |
| − | 1 | 6 | |
| 8 | |||
| − | 8 | ||
| 0 |
16 ÷ 4 = 4, the point goes in as the 8 comes down, and 8 ÷ 4 = 2. So 16.8 ÷ 4 = 4.2, and 1.68 ÷ 0.4 = 4.2 as well.
Why it works
Moving both points one place multiplies both numbers by 10, and that never changes a division: 1.68 ÷ 0.4 and 16.8 ÷ 4 ask the same question, the way 6 ÷ 2 and 60 ÷ 20 do. It just makes the divisor something you can use the times tables on.
The point goes straight up because every digit of the answer sits above the digit it came from. A digit worked out from the tenths of the dividend is a number of tenths, so it has to be in the tenths place of the answer too.
Adding zeros changes nothing either: 127, 127.0 and 127.00 are the same number. Writing them gives the remainder something to turn into: 3 ones left over are 30 tenths.
Where mistakes happen
- Moving only the divisor's point. Both points move, by the same number of places, or the question changes.
- Leaving out the 0 at the start. 2.4 ÷ 6 is 0.4; writing just .4, or 4, is how the point goes missing.
- Putting the point in too early or too late. It goes into the answer at the moment the first digit after the dividend's point comes down. Not before, and not at the end.
- Stopping with a remainder when the question wants a decimal. Add a 0 and carry on.
Questions people ask
Does it always come out exactly?
No. 1 ÷ 3 is 0.333… for ever, because the same remainder keeps coming back. When a remainder repeats, the digits of the answer will repeat too; that is a recurring decimal.
Why can't I just divide by 0.4?
You can in principle, but every step would ask how many 0.4s go into something, which is hard to do from a times table. Moving the points turns it into a times-table question without changing the answer.
Should I give a remainder or a decimal?
Whichever the question asks for. 127 sweets shared between 4 children is 31 each with 3 left over; 127 metres of rope cut into 4 equal pieces is 31.75 metres each.