What is a Truncation Error?

A truncation error is a mistake that occurs in data calculations when a value is not as precise as it should be, and therefore leads to a final answer that is either imprecise or incorrect. Data values that contain truncation errors may be accurate, but they may not be precise. The existence of these errors highlights the difference between accuracy and precision, which are distinct qualities in data. Accuracy is defined by how close a data point is to its true value, and precision is defined by how reproducible a result is. A data value without a truncation error is usually accurate and precise, while a value obtained with this error involved is often accurate but not precise, because it cannot be reproduced consistently.

In science and engineering, seemingly small truncation errors have the potential to create major problems. For example, if something was being measured in units of ten-thousandths of a meter, a value of 1.0001 meters would be both accurate and precise, but a measurement of 1.0 meters would not be precise enough and would therefore contain a truncation error. That ten-thousandth of a meter difference could cause problems on its own or be compounded in calculations so further measurements may lose both accuracy and precision. In experiments or machines where exact interaction of parts is crucial to prevent friction, measure angles, or handle other important calculations, these errors can be costly.

Truncation errors can almost always be avoided by ensuring that calculations and measurements use the correct number of significant figures. If the final answer to a calculation should have four significant figures, for example, all intermediate calculations should have at least that number of significant figures at every step. As a rule, any value inside intermediate calculations should not be truncated because if a value is cut off incorrectly, a truncation error results that could skew the results of the entire calculation.

For most everyday calculations and measurements, truncation errors do not have the potential to cause significant damage. Cutting three feet of string instead of 3.05 feet would not make a difference to a child playing string games in the backyard. Certain instances exist in which someone may wish to be aware of how easy the truncation error can be made. For example, truncating $100.02 US Dollars (USD) to $100 USD for an insurance payment could cause an otherwise savvy consumer to lose coverage because the payment was imprecise.