Note that the quotient returned will not necessarily have the same value as the whole part of dividing self by x with the '/' operator, because this division handles rounding differently. In particular, the '/' operator will perform the appropriate rounding on the quotient if the quotient has insufficient precision to represent the exact result. This routine, in contrast, does NOT round the quotient, but merely truncates any trailing digits that cannot be represented in the result's precision. The reason for this difference is that it ensures that the relation (dividend=quotient*x+remainder) holds, which would not always be the case if the quotient were rounded up.

Note also that the remainder will not necessarily be less than the divisor. If the quotient cannot be exactly represented (which occurs if the precision of the quotient is smaller than its scale), the remainder will be the correct value so that the relationship above holds, rather than the unique remainder that is smaller than the divisor. In all cases where there is sufficient precision to represent the quotient exactly (to the units digit only, since the quotient returned from this method will always be an integer), the remainder will satisfy the relationship AND will be the unique remainder with absolute value less than the divisor.