Definition:Approximation

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Definition

An approximation is an estimate of a quantity.

It is usually the case that there exists some knowledge about the accuracy of the estimate.

The notation:

$a \approx b$

indicates that $b$ is an approximation to $a$.



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Examples

$\dfrac {22} 7$ as an Approximation for Pi

$\dfrac {22} 7$ is a convenient approximation to $\pi$:

$\dfrac {22} 7 = 3 \cdotp \dot 14285 \dot 7$


$x$ as an Approximation for $\sin x$ for small $x$

For small values of $x$ measured in radians:

$\sin x \approx x$


$1.414$ as an Approximation for $\sqrt 2$

$1 \cdotp 414$ is an approximation to $\sqrt 2$.


Also see

  • Results about approximations can be found here.


Linguistic Note

The verb form of approximation is approximate, whose meaning is:

to find a value or expression for a quantity within a specified degree of accuracy

and whose pronunciation is something like ap-prox-i-mayt.

The adjectival form of approximation is also approximate, and means:

within a specified degree of accuracy

but its pronunciation is more like ap-prox-i-mut.

Note the difference in the final syllable.


Sources

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