Question

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`?

Answer 1

`-9/5, -0.75, 2/3, pi/3, 2 1/4, sqrt(8)`

Explanation:

Note that:

`3 < pi < 6 " "` so `" "1 < pi/3 < 2`

`2.7^2 = 7.29 " "` so `" " 2.7 = sqrt(7.29) < sqrt(8)`

So we find:

`color(blue)(-9.5) = -1.8 < color(blue)(-0.75) < 0 < color(blue)(2/3) < 1 < color(blue)(pi/3) < 2 < color(blue)(2 1/4) = 2.25 < 2.7 < color(blue)(sqrt(8))`

So the correct order is:

`-9/5, -0.75, 2/3, pi/3, 2 1/4, sqrt(8)`