GNU Emacs Calc 2.02 Manual
3.7.12 Arithmetic Tutorial Exercise 1
Dividing two integers that are larger than the current precision may
give a floating-point result that is inaccurate even when rounded
down to an integer. Consider 123456789 / 2 when the current
precision is 6 digits. The true answer is 61728394.5, but
with a precision of 6 this will be rounded to
12345700. / 2. = 61728500..
The result, when converted to an integer, will be off by 106.
Here are two solutions: Raise the precision enough that the
floating-point round-off error is strictly to the right of the
decimal point. Or, convert to fraction mode so that 123456789 / 2
produces the exact fraction 123456789:2, which can be rounded
down by the F command without ever switching to floating-point