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I have studied that any real number $x$ can be approximated by rationals since the rationals are dense on the real line.

I am searching for an example . Can anyone show this with an example?

Thanks for any help.

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    @JonasMeyer Sorry sir i didn't reply. I am cleared with this now.Ya The Archimedean property leads to the density of rationals in $\mathbb{R}$" and density of irrationals in \$mathbb{R}$" i.e. between any two distinct real numbers there is a rational number and also between any two distinct real numbers there is an irrational number.2012-05-25

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$3$ is rational number that approximates $\pi$ with an error less than $1$.

$3.1$ is rational number that approximates $\pi$ with an error less than $1/10$.

$3.14$ is rational number that approximates $\pi$ with an error less than $1/100$.

$3.141$ is rational number that approximates $\pi$ with an error less than $1/1000$.

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    +1 But let's not forget that $355/113$ is better than $314159/100000$.2012-05-22