Truncation means dropping digits from a number. In the following examples, numbers are truncated to 2 decimal places.

12.28392 ~ 12.28
23.45672 ~ 23.45
-6.39812 ~ -6.39

Truncation is rarely useful in statistics.

Rounding is NOT truncation. Rounding means dropping digits from a number AND adjusting the remaining digits according to some rule. The rule usually is to make the rounded value as close to the original value as possible. In the following example, numbers are rounded to two decimal places.

12.28392 ~ 12.28
23.45672 ~ 23.46
-6.39812 ~ -6.40

Ambiguous cases occur when the number to be rounded is exactly midway between two other values. In that case, a rounding convention must be followed. In this class, we will adopt the convention of "rounding to the even digit." Examples follow.

12.275 ~ 12.28
12.285 ~ 12.28
28.135 ~ 28.14
-7.865 ~ -7.86
18.065000000000000000 ~ 18.06
18.065000000000000001 ~ 18.07