Long division of decimals works almost exactly the same as long division of whole numbers. Long division of decimals just involves an extra step of moving decimal points, which is necessary when you're dividing by a decimal number.
- Move the decimal in the divisor as many places to the right as necessary
The objective is to make the number in question a whole number. After doing this, move the decimal in the dividend the same number of places. The ratio is the same. For example, if you are dividing 72.9 by 8.1, the decimal point needs to move a place to the right and yield 729/81.
- Proceed with long division
Write the number of times the divisor goes into the dividend, then multiply this quotient by the divisor, and subtract the result from the dividend. Repeat until all digits have been accounted for. In the example, this yields a quotient of 9 with no remainder.
- Replace the decimal point
The decimal point should be placed where it was originally. In the quotient, place the decimal point directly above the decimal in the dividend.
- Check the result
Multiply the quotient by the divisor. It should be equal to the dividend. If not, you need to rework the problem.