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.
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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