# False precision

False precision occurs when numerical data is 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.

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 by the precision of that data. 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.

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

• 'Bobo the Elephant weighs 10000 kilograms. I weigh 79 kilograms. Therefore, if I sat on Bobo, we would weigh 10079 kilograms.'
• 'There were about two hundred people at the party when it started. Three of them left early, so we should set one hundred and ninety-seven places for dinner.'
• In the Wikipedia article on Manhattan, a population of 1,537,195, with a land area of 59.5 km² (23.0 mi²), is stated to have a population density of 25,849.9/km² (66,940.1/mi²).
• 'Two years ago an article was published stating that the dinosaurs died out 65 million years prior, which means the dinosaurs died out 65,000,002 years ago.'
• The Wikipedia article Mikoyan-Gurevich MiG-21 stated "Thrust 69.58 kN 15,650 lbf" in the table for this fighter plane. This is a trickier one; just looking at those numbers will not give you any notice that there is false precision involved. The problem comes in, however, because both of these numbers are the result from an unstated original in units different from either of the ones stated here: 7,100 kilograms-force times 9.8 m/s² to get 69,580 newtons, and 7,100 kgf times 2.2046 lbf/kgf to get 15652.66 lbf, rounded slightly but not enough. Note that the conversion factor used to convert kgf to kN is not precise enough to get 4 significant digits in the result (the exact conversion factor is 1 kgf = 9.80665 N), even if the measurement of the thrust were 7.100 megagrams-force, with both zeros significant.

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