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 < -(1)/(3)`

As for the positive numbers, we have to order
`√(7),\ √(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 = √(3)^2 < 7 = √(7)^2 < 26.01 = 5.1^2`.

So, the ordered list is the following:

`-2.3,\ -(1)/(3), √(3),\ √(7),\ 5.1`

Answer 2

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