d65d6fb6-c29c-4a85-821a-b028853311d5 8 3 5 false true decimal

&[DATE] &[TIME] - &[FILENAME]

Random numbers

D 10000 Random :

Dr D 4 round vectorize eval :

Round the numbes to 4 digits

S.0 Dr sum : 4999.9443

Sum of the numbers without further rounding

S.away Dr 3 round vectorize sum : 5000.46300000001

Sum of the numbers with further rounding to 3 digits away from zero

S.away S.0 - S.0 / ppm 104

S.even Dr 1000 * round Maxima sum 1000 / : 4999.975

Sum of the numbers with further rounding to 3 digits to even

S.even S.0 - S.0 / ppm 6.14

The error introduced by round to even is much smaller than that for round away from zero. Also, the error for round away from zero is always positive whereas that of round to even may be positive or negative.

Note that intermediate rounding to 4 digits is essential for the demo. The more digits you cut away the less is the difference between the two rounding options. In the demo, just one digit is cut away.