How do you divide decimals?

Dividing a decimal works just like ordinary division. The only new thing is the decimal point, and there are three situations to know.

1. A decimal divided by a whole number. Use short division or long division, and put the decimal point in the answer directly above the decimal point in the number you are dividing. Then divide each digit as usual. For 8.76 ÷ 3: 8 ÷ 3 = 2 remainder 2; carry the 2 to make 27; 27 ÷ 3 = 9; then 6 ÷ 3 = 2. The answer is 2.92. Check: 2.92 × 3 = 8.76.

If there is a remainder at the end, you do not have to stop. Write zeros after the last decimal digit (8.5 is the same as 8.50 or 8.500) and keep dividing. That is how 5 ÷ 4 becomes 5.00 ÷ 4 = 1.25. Some divisions never end: 10 ÷ 3 = 3.333…, where the 3 repeats forever. Then you round, for example to 3.33.

2. Dividing by 10, 100 or 1,000. Each digit moves to a place value that is 10, 100 or 1,000 times smaller: one place right for ÷ 10, two for ÷ 100, three for ÷ 1,000. It looks as if the decimal point moves left. 45.3 ÷ 10 = 4.53, 45.3 ÷ 100 = 0.453 and 45.3 ÷ 1,000 = 0.0453. Fill empty places with zeros.

3. A number divided by a decimal. Nobody divides by 0.6 directly. Instead, multiply both numbers by the same power of 10 so that the divisor becomes a whole number. The answer does not change, because you are scaling both numbers equally (72 tenths shared into groups of 6 tenths is the same as 72 into groups of 6):

7.2 ÷ 0.6 = 72 ÷ 6 = 12

Move the point as many places as there are decimal places in the divisor (the number you divide by), and move it the same number of places in the other number too. For 4.8 ÷ 0.12, the divisor has two decimal places, so multiply both by 100: 480 ÷ 12 = 40.

A useful surprise: dividing by a number less than 1 gives a bigger answer. 6 ÷ 0.5 = 12, because there are 12 halves in 6.

The rule in one line: make the divisor a whole number, then divide as normal. There is no special formula to learn beyond that.

What is the rule for dividing decimals?#

If the divisor is a whole number, divide normally and put the point straight above. If the divisor is a decimal, multiply both numbers by 10, 100 or 1,000 until the divisor is whole, then divide.

How do you divide decimals by whole numbers?#

Divide digit by digit as in ordinary division and line up the decimal point in the answer with the point in the dividend. For example, 9.6 ÷ 4 = 2.4.

How do you divide by 10, 100 and 1,000?#

Move each digit one, two or three places to the right (the decimal point seems to jump left). 3.8 ÷ 10 = 0.38, 3.8 ÷ 100 = 0.038, 3.8 ÷ 1,000 = 0.0038.

What happens when the divisor is bigger than the number you are dividing?#

The answer is less than 1. Add zeros after the decimal point and divide: 3 ÷ 4 = 3.00 ÷ 4 = 0.75.

What do you do with a remainder when dividing decimals?#

Do not write "r". Add a zero to the end of the dividend and keep dividing. If it never ends, round the answer, for example 2 ÷ 3 ≈ 0.67.

How do you divide by 0.1, 0.01 and 0.001?#

Dividing by 0.1 is the same as multiplying by 10, by 0.01 the same as multiplying by 100, and by 0.001 the same as multiplying by 1,000. So 4.7 ÷ 0.1 = 47.

How can I divide decimals without a calculator?#

Make the divisor a whole number, then use short or long division. Always estimate first (7.9 ÷ 2.1 is about 8 ÷ 2 = 4) so you can spot a misplaced point.