# False precision

False precision (also called overprecision, fake precision, misplaced precision and spurious accuracy) occurs when numerical data are presented in a manner that implies better precision than is actually the case; since precision is a limit to accuracy, this often leads to overconfidence in the accuracy as well.[1]

In science and engineering, convention dictates that unless a margin of error is explicitly stated, the number of significant figures used in the presentation of data should be limited to what is warranted by the precision of those data. For example, if an instrument can be read to tenths of a unit of measurement, results of calculations using data obtained from that instrument can only be confidently stated to the tenths place, regardless of what the raw calculation returns or whether other data used in the calculation are more accurate. Even outside these disciplines, there is a tendency to assume that all the non-zero digits of a number are meaningful; thus, providing excessive figures may lead the viewer to expect better precision than actually exists.

However, in contrast, it is good practice to retain more significant figures than this in the intermediate stages of a calculation, in order to avoid accumulated rounding errors.

False precision commonly arises when high-precision and low-precision data are combined, and in conversion of units.

## Examples

100.000%
• There are numerous variations of a joke which can be summarized as follows: A tour guide at a museum says a dinosaur skeleton is 100,000,005 years old, because an expert told him that it was 100 million years old when he started working there 5 years ago.
• "European authorities estimated that the bomb used 220 pounds of explosive." In this example, European authorities, who express measurements in SI units (the metric system), probably estimated that the bomb used 100 kg of explosives. Such estimates are necessarily subject to great uncertainty. When converted by the American media to pounds, the added precision suggests greater accuracy in the estimation of the bomb's size than warranted. A better way to state this is as follows: "European authorities estimated that the bomb used 100 kg (about 220 lbs) of explosives."
• Average "normal" human body temperature (oral measurement) was previously considered to be 98.4°F in the UK. This is approximately 37°C, which when converted back to Fahrenheit becomes the different value 98.6°F popular in the US. Modern studies show that none of these values is accurate to one tenth of a degree Fahrenheit, even for the hypothetical average person (see Human body temperature).
• On some[which?] commercial flights, there is a display showing a rotating set of data, such as the current speed and altitude, in different languages for the entertainment of passengers. In the metric system, one can sometimes observe the altitude jump instantaneously from, for example, 9144 meters to 8839 meters. These values correspond to 30000 feet and 29000 feet, respectively. The informed observer may therefore assume that the true measured altitude is first rounded to the closest multiple of 1000 feet, then converted to metric with an accuracy of 1 meter.[citation needed]