Answer
$\frac{4}{9}$
Work Step by Step
To order, convert all numbers to decimals.
$\frac{9}{20}=\frac{9\times5}{20\times5}=\frac{45}{100}=0.45$
$\ \ \ \,0.4\overline4$
$9\big)\overline{4.0\underset\downarrow0}$
$\ \ \ \ \,\underline{36}$
$\ \ \ \ \ \ \ 40$
$\ \ \ \ \ \ \,\underline{36}$
$\ \ \ \ \ \ \ \ \ 4$
$0.4\overline4\lt0.45\lt0.456$
so
$\frac{4}{9}$
