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The detailed guide below is currently available in English.
How the remainder and decimal forms relate
Long division asks how many whole times the divisor fits into the dividend, and what is left over. Dividing 985 by 4 gives 246 with a remainder of 1, because 4 × 246 = 984. The leftover 1 is where the decimal form comes from: bring down a zero and keep dividing, so the remainder becomes 10 ÷ 4 more tenths, and 985 ÷ 4 = 246.25. The step table shows each digit of the dividend being brought down, the working value it joins, and the remainder carried forward.
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What does a remainder of zero mean?
The divisor divides the dividend evenly, so the quotient is exact and the decimal answer simply ends. For example, 156 ÷ 12 gives 13 with no remainder.
Why do the same remainders start repeating in some problems?
A remainder is always a whole number from 0 up to one less than the divisor. If a division never hits zero, some remainder must eventually repeat, and from that point the decimal digits repeat in a cycle — like 10 ÷ 3 giving 3.333…