Art of Problem Solving

Approximation: Difference between revisions

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Approximating things
'''Approximation''' is a technique used to acquire a value that is close, but not exact. It is used to make some problems easier to calculate, such as large numbers or long decimals.


== Definition ==
== Example ==  
Approximately equal
 
'' From [//https://artofproblemsolving.com/wiki/index.php/2024_AMC_10B_Problems/Problem_3 2024 AMC 10B #3] ''
 
For how many integer values of <imath>x</imath> is <imath>|2x| \leq 7 \pi</imath>
 
In this problem, <imath>7\pi</imath> can be approximated to be just over 21, since pi is close to 3.


== LaTeX ==
== LaTeX ==
The approximation symbol (<math>\approx</math>) symbol can be created with the following LaTeX:
The approximation symbol (<imath>\approx</imath>) can be created with the following LaTeX:


<code>$ \approx $</code>
<code>$ \approx $</code>

Latest revision as of 14:59, 10 November 2025

Approximation is a technique used to acquire a value that is close, but not exact. It is used to make some problems easier to calculate, such as large numbers or long decimals.

Example

From 2024 AMC 10B #3

For how many integer values of $x$ is $|2x| \leq 7 \pi$

In this problem, $7\pi$ can be approximated to be just over 21, since pi is close to 3.

LaTeX

The approximation symbol ($\approx$) can be created with the following LaTeX:

$ \approx $

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