# Question #f8d03

Oct 13, 2016

The easiest way to solve this is reverting to the decimal expression of the numbers given

#### Explanation:

These are all rational numbers, and they have a decimal expression that is either finite or infinite periodic. Let's see:

$- 0.6$; this is the decimal expression, nothing to do

$- \frac{5}{8} = - 0.625$; simply calculating 5 divided by 8

$- \frac{7}{12} = - 0.583333 \ldots$; periodic, again by division

$- .72 = - 0.72$; this is the decimal expression, nothing to do

Now let's see what happens with the order of these numbers. If we consider positive numbers, say $1$ and $2.3$, we know that $1 < 2.3$, but if we add first $- 1$ to both sides of the inequality we get

$0 < 2.3 - 1$, and now if we add -2.3 to both sides we get:

$- 2.3 < - 1$. So, if two numbers $a$ and $b$ are such that $a < b$, their opposites are in the reverse order $- b < - a$.

Now we can order the numbers above:
$- 0.72 < - 0.625 < - 0.6 < - 0.58333 \ldots$