Notice that all of the numbers given are written in different forms. Let's rewrite each of them as decimals, and then try to compare them.
Rewriting the Numbers
We know that -3 and 5.5 are already in decimal form. Therefore, we do not need to change them. Let's focus now on sqrt(31). To convert the square root into decimal we will use a calculator.
We found that sqrt(31)≈ 5.57. Next, we will rewrite sqrt(11) in the same way.
We know that sqrt(11)≈ 3.32. Let's rewrite our last expression, - 6011, we will use a calculator once again.
We found that - 6011≈ -5.45.
Ordering
To order the values, we will graph them on the number line.
Let's start with - 3.
Next, let's plot sqrt(31)≈ 5.57. To do this, we will find 5 on the number line and move about 0.6 steps in the positive direction.
To plot sqrt(11)≈ 3.32. we will find 3 on the number line and move about 0.32 steps in the positive direction.
Now, let's graph 5.5. Notice that we have to find 5 on the number line and move 0.5 steps in the positive direction. This means that 5.5 will lie before sqrt(31) on the number line.
Finally, let's draw - 6011≈ -5.45 in the same way as before.
To order numbers from least to greatest, we can read the graph from left to right.
-60/11, - 3, sqrt(11), 5.5, sqrt(31)
