A rounding habit quietly halved the Vancouver Stock Exchange index
In 1982 the Vancouver Stock Exchange launched a new index at 1000. Twenty-two months later it stood near 520, even though the market seemed to be climbing. The culprit was not a crash but arithmetic: each of thousands of daily recalculations chopped the result to three decimal places, and the tiny losses piled up.
Rounding means swapping a number for a simpler, nearby value, such as $23.45 for $23.4476 or 1.414 for the square root of 2. It makes figures easier to communicate and stops a measurement from pretending to more precision than it has: a count known only to within a few hundred is more honest as about 123,500. But every rounding introduces a small error, and in long chains of calculation those errors can accumulate, sometimes enough to make a result meaningless.
That is what happened in Vancouver. The index was always truncated, meaning the extra digits were simply dropped, so every recalculation nudged it downward. When the same period was recomputed by rounding to the nearest thousandth instead, the value came out at 1098.892 rather than 524.811.
There are many ways to round because no method has every desirable property. Directed methods always push the same way: rounding down, up, toward zero or away from it. These are used in interval arithmetic and are often required in financial work. Rounding to the nearest whole number is fairer, since for each fraction pushed down, like 0.268, a partner such as 0.732 gets pushed up by the same amount. The awkward case is exactly one half, which needs a tie-breaking rule. Round half up is common, though programming languages such as Java and Python use that name for rounding halves away from zero.
Computers face a deeper puzzle called the table-maker's dilemma: for functions like sines and logarithms, you cannot know in advance how many extra digits are needed to decide which way to round. The wavy equals sign used for approximations was introduced by Alfred George Greenhill in 1892.
Source: Rounding
