gradi e radianti

Ho usato correttamente le unità di misura?

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\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{siunitx}
\sisetup{output-decimal-marker={,},
detect-all,
list-separator = {;~},
list-final-separator = { ~\text{e}~ },
list-pair-separator = { ~\text{e}~ },
range-phrase = { \translate{a (numerical range)} },
detect-weight, detect-display-math, detect-inline-weight=math,fraction=nice}
\begin{document}
Convertire \SI[round-precision=3,round-mode=places]{2.856}{\radian} in gradi sessagesimali

\[\alpha=\dfrac{180}{\pi}\cdot\rho=\dfrac{180}{\pi}\cdot\SI[round-precision=3,round-mode=places]{2.856}{\radian}\approx\ang[round-precision=4,round-mode=places]{163.6367463} \]
Iniziamo con
$\alpha=\ang{163}+\ang[round-precision=4,round-mode=places]{0.6367463}$
\begin{align*}
\alpha^{\degree }&=\ang{163}\\
\alpha^{\arcminute}&=\ang[round-precision=4,round-mode=places]{0.6367463;;}\cdot 60=\ang[round-precision=4,round-mode=places]{;38.20477736;}=\ang{;38;}\\
\alpha^{\arcsecond}&=\ang[round-precision=4,round-mode=places]{;0.204777358;}\cdot 60=\ang{;;12}\\
\end{align*}
abbiamo quindi
\[\alpha=\ang[round-precision=4,round-mode=places]{163.6367463}=\ang{163;38;12} \]
\end{document}
`
o sono stato troppo formale
ciao