When Remainders Become Decimals

A division can finish with a remainder... or can it? Add a decimal point and zeroes, and that leftover can keep dividing. The answer becomes more precise with every new decimal place you reveal.

Picture forty-seven counters shared equally between four trays. Each tray gets eleven counters, with three left over. So forty-seven divided by four is eleven remainder three. That remainder is not automatically the final answer. The question tells you how to report it. To continue, write a decimal point after eleven. Add a zero after forty-seven, making four hundred and seventy tenths in the working. Bring down the zero beside the remainder three. Now divide thirty by four. Seven fits, with two left. The seven means seven TENTHS, not just seven. Its column gives its place value. You can add another zero and continue again. Twenty divided by four is five, so the exact answer is eleven point seven five. If the question asks for fewer decimal places, look at the NEXT digit, then round once.

Let's work through an example. Calculate fifty-three divided by eight. Give your answer to one decimal place. This is one division, so there is no chain of operations to work through from left to right. Eight fits into fifty-three six times, because six eights are forty-eight. Subtract, and five remains. Write fifty-three point zero, then put the answer's decimal point directly above it. Bring down the zero. Fifty divided by eight is six, with two left. The six sits in the tenths column. We need one decimal place, so inspect the next digit. Add another zero. Twenty divided by eight is two, with four left. The hundredths digit is two. Two is below five, so the tenths digit stays six. The required answer is six point six.

Divide carefully, extend a remainder with zeroes when needed, and let the stated accuracy control your final answer. Keep each digit in its proper place - and you will divide with confidence!