Approximation/Examples/22 over 7

Theorem

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

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

$\ds \dfrac {22} 7$

$=$

$\ds 3 \cdotp \dot 14285 \dot 7$

$\ds \pi$

$\approx$

$\ds 3 \cdotp 14159265$

$\ds \leadsto \ \ $

$\ds \dfrac {22} 7 - \pi$

$\approx$

$\ds 0 \cdotp 0012645$

$\ds \leadsto \ \ $

$\ds \dfrac {\frac {22} 7 - \pi} \pi$

$\approx$

$\ds 0 \cdotp 0004025$

$\ds $

$\approx$

$\ds 0 \cdotp 04025 \%$

$\blacksquare$