Consider the given set of numbers.
{8/5,1.4,-17,10^2}
In order to compare them, we will rewrite them all to be in decimal form. The numbers -17 and 1.4 are already in decimal form, so we do not need to change these numbers at all. Let's start by calculating 10^2.
10^2=100
Now, we can calculate 85 by rewriting this fraction.
Finally, let's compare them. We can see that ordering from the least to the greatest gives us:
{-17,1.4,1.6,100}
⇓
{-17, 1.4, 8/5, 10^2 }
Alternative Solution
A different way of thinking...
We could have arrived to the same conclusion if we think about the given numbers for a little while. First of all, -17 is the only negative number, so it must be the least. Then, to decide which is greater, 1.4 or 85, we can rewrite 1.4 as a fraction.
Since 1.4= 75 we know that 1.4= 75 < 85
We also know that any real number greater than 1 will increase rapidly when raised to a positive integer power. Thia means that, 10^2 must be our greatest number. Therefore, the ordering once again gives us:
{-17, 1.4, 8/5, 10^2 }
