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.

**Answer**

In a mathematical context, the word would be ** exact**. An exact calculation always gives the mathematically expected result. The opposite is

**: 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**

*approximate**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).

**Attribution***Source : Link , Question Author : user2246 , Answer Author : Gilles ‘SO- stop being evil’*