We often use approximations like: “It’s about thirty degrees outside.” But an article explains how roundoff error can actually be devastating as well as the foundation for future success.
An entry in Wolfram MathWorld includes the following:
An egregious example of roundoff error is provided by a short-lived index devised at the Vancouver stock exchange. At its inception in 1982, the index was given a value of 1000.000. After 22 months of recomputing the index and truncating to three decimal places at each change in market value, the index stood at 524.881, despite the fact that its “true” value should have been 1009.811.
People who invested in that index fund must have been pretty upset that half of their money had vanished due to an arithmetic mistake! And in fact, the Vancouver Stock Exchange corrected the price in only one day. They also determined they needed a more comprehensive process for designing and reviewing index funds.
Failure is the secret to success. We sometimes need to make tremendous mistakes to realize how to get better. Sometimes, those errors are something as small as a rounding error, but they add up over time. They help us realize how we can and should improve.