First of all, negative numbers will surely come before positive ones. So, let's compare -2.3 and -1/3.
One is a number, one is a fraction. You can either turn the fraction to number, or the number to fraction. The first option is surely easier: we have -1/3 = -0.333...
So, -1/3 is closer to 0 than -2.3, so we have [tex] -2.3 < -\frac{1}{3} [/tex]
As for the positive numbers, we have to order [tex] \sqrt{7},\ \sqrt{3},\ 5.1 [/tex]. When dealing with positive numbers, it is true that [tex] x < y \implies x^2 < y^2 [/tex]. So, we can square the numbers to get rid of the roots: we have
[tex] 3 = \sqrt{3}^2 < 7 = \sqrt{7}^2 < 26.01 = 5.1^2 [/tex].
So, the ordered list is the following:
[tex] -2.3,\ -\frac{1}{3}, \sqrt{3},\ \sqrt{7},\ 5.1 [/tex]
