What isTruncation error in numerical flow scheme?

Answer 1

Truncation error is the error introduced when an series is shortened, i.e. "truncated", before it is complete.

For instance, 1/3 is 0.333333333...etc., but we place limits on how many decimal digits to use, so that introduces an error.

Another example is a large number, such as 240-1. That number, in binary, is 111111111111111111111111111111111111111, or 39 1's in a row. Place that in a floating point number, and you might only get 22 bits of resolution, so the internal value might only be, in binary, 1.1111111111111111111111x238. Rewriting that, you get 111111111111111111111110000000000000000, which is not exactly correct. The first number is 1,099,511,627,775. The second number is 1,099,511,496,704, an error of 131,071.

A third example is the seemingly innocuous representation of 0.1 in binary. In decimal, 0.1 is terminating and non repeating. Express it in binary, however, and you get 0.0001100110011001100...etc. Place that in a floating point number, and truncation error will make it like something like 0.0999999940395355224609375, in a 22 bit format, which is not exactly 0.1.