Write the following numbers in order of size, starting with the smallest. $\left(\dfrac{3}{10}\right)^2$, $-\dfrac{21}{90}$, $90\%$, $-0.23$, $\sqrt{0.3}$

1. Convert each number to a comparable decimal form.

$\left(\dfrac{3}{10}\right)^2=0.3^2=0.09$

$-\dfrac{21}{90}=-\dfrac{7}{30}=-0.2333\ldots$

$90\%=0.9$

$-0.23=-0.23$

$\sqrt{0.3}=0.5477\ldots$

2. Arrange the decimal values from smallest to largest.

Comparing the decimal values:

$-0.2333\ldots < -0.23 < 0.09 < 0.5477\ldots < 0.9$

Therefore,

$-\dfrac{21}{90} < -0.23 < \left(\dfrac{3}{10}\right)^2 < \sqrt{0.3} < 90\%$