Truncation errors occur when data values are not precise enough, leading to inaccurate final answers. Precision and accuracy are distinct qualities in data. In science and engineering, small truncation errors can cause major problems. These errors can be avoided by using the correct number of significant figures. For everyday calculations, truncation errors are not significant, but in some cases, they can cause problems, such as in insurance payments.
A truncation error is an error that occurs in data calculations when a value isn’t as precise as it should and thus leads to an inaccurate or incorrect final answer. 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. Precision 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 can create major problems. For example, if something was 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 the calculations so that further measurements may lose both accuracy and precision. In experiments or machines where the exact interaction of parts is critical for preventing friction, measuring angles, or handling other important calculations, these mistakes can be costly.
Truncation errors can almost always be avoided by making sure that calculations and measurements use the correct number of significant figures. If the final answer to a calculation must have four significant figures, for example, all intermediate calculations must have at least that number of significant figures at each step. As a rule, any value within intermediate calculations should not be truncated because if a value is trimmed incorrectly, a truncation error occurs which could skew the results of the entire calculation.
For most everyday calculations and measurements, truncation errors cannot cause significant harm. Cutting three feet of rope instead of 3.05 feet would make no difference to a kid playing rope games in the backyard. There are some cases where someone might want to be aware of how easy it is to make the truncation error. For example, truncating $100.02 United States Dollars (USD) to $100 USD for an insurance payment could cause an otherwise savvy consumer to lose coverage because the payment was inaccurate.
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