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Is there a word or phrase in English that means accurate to an infinite level of precision? For example, the measurement of a length that is 'perfectly accurate' records the length down to its final decimal place.

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  • Just for benefit of people seeking by title - the phrase describing perfectly accurate to be used in common-day English, as opposed to (requested) "scientific accuracy" is Spot-on. – SF. Oct 1 '13 at 12:44
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In a mathematical context, the word would be exact. An exact calculation always gives the mathematically expected result. The opposite is approximate: an approximate calculation gives a result that is close to the exact result, but not identical. For example, the circumference of a circle of radius 1 is exactly 2π, which is approximately 6.283. These words are also used in computer contexts: for example, financial calculations are usually done with exact arithmetic (using integers or fixed-point decimal numbers, with well-defined rounding rules), whereas physical calculations are usually done with inexact or approximate arithmetic (using floating-point numbers, with rounding rules that are intended to maximize the precision of the result but not always to be perfectly reproducible).

Strictly speaking, a physical measurement cannot be exact (the length of a stick has no “final decimal place”). However you can still use the word exact to mean that the precision of the measurement is so great that the uncertainty about the measured quantity will never matter. You can also use perfectly accurate in this context (again, meaning so accurate that any inaccuracy is irrelevant).

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  • "Precise" can be another option. – Mistu4u Oct 1 '13 at 12:26
  • @Mistu4u No, precise is a relative term, not an absolute term. A measurement to 1% accuracy is more precise than a measurement to 10% accuracy. A measurement that is said to be precise may not be perfectly accurate, no more than a tall person is infinitely high. – Gilles 'SO- stop being evil' Oct 1 '13 at 12:33
  • @Gilles, that's only because of the dilution of the language. Apparently "precise" has lost its precision. thefreedictionary.com/precise 2. Exact, as in performance, execution, or amount; accurate or correct: a precise measurement; a precise instrument. – TecBrat Oct 1 '13 at 12:43
  • @TecBrat True, there are contexts where the two words can be used interchangeably, but not all of them. A precise clock might stay accurate for months; a very precise clock might stay accurate for a lifetime. (Notice the qualifier very? You can't use it with exact, except for stylistic effect.) An exact clock would always tell the time. As far as I know, precise was never specifically about exactness, so it isn't a matter of dilution of language — rather a general manifestation of imprecision (but not inexactness), where a relative term gets a sideline as an absolute. – Gilles 'SO- stop being evil' Oct 1 '13 at 12:51
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    @Giles: I disagree - and so does OED, which defines precisely: With precise or exact correspondence, in every detail; with complete accuracy. I think you're overly influenced by mathematical contexts where "precision" is a "variable" attribute relating to how accurate a value is. – FumbleFingers Oct 1 '13 at 13:45

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