How do you order the following from least to greatest without a calculator 2/3, -0.75, sqrt8, -9/5, pi/3, 2 1/4?

Sep 2, 2016

$- \frac{9}{5} , - 0.75 , \frac{2}{3} , \frac{\pi}{3} , 2 \frac{1}{4} , \sqrt{8}$

Explanation:

Note that:

$3 < \pi < 6 \text{ }$ so $\text{ } 1 < \frac{\pi}{3} < 2$

${2.7}^{2} = 7.29 \text{ }$ so $\text{ } 2.7 = \sqrt{7.29} < \sqrt{8}$

So we find:

$\textcolor{b l u e}{- 9.5} = - 1.8 < \textcolor{b l u e}{- 0.75} < 0 < \textcolor{b l u e}{\frac{2}{3}} < 1 < \textcolor{b l u e}{\frac{\pi}{3}} < 2 < \textcolor{b l u e}{2 \frac{1}{4}} = 2.25 < 2.7 < \textcolor{b l u e}{\sqrt{8}}$

So the correct order is:

$- \frac{9}{5} , - 0.75 , \frac{2}{3} , \frac{\pi}{3} , 2 \frac{1}{4} , \sqrt{8}$