Question

Order the following numbers from least to greatest. square root of 7, -2.3, square root of 3, 5.1, -1/3. Please help! The last one is a fraction not an equation.

Answer 1

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 $-2.3 < -\frac{1}{3}$

As for the positive numbers, we have to order $\sqrt{7},\ \sqrt{3},\ 5.1$. When dealing with positive numbers, it is true that $x < y \implies x^2 < y^2$. So, we can square the numbers to get rid of the roots: we have

$3 = \sqrt{3}^2 < 7 = \sqrt{7}^2 < 26.01 = 5.1^2$.

So, the ordered list is the following:

$-2.3,\ -\frac{1}{3}, \sqrt{3},\ \sqrt{7},\ 5.1$

Answer 2

-2.3, -1/3, square root of 3, square root of 7, 5.1