Let's determine which number in the set [tex]\(-6 \frac{2}{3}, -6.6, -6.06, -6 \frac{2}{5}\)[/tex] is the greatest.
Step 1: Convert each fraction to its decimal form
1. Convert [tex]\(-6 \frac{2}{3}\)[/tex]:
[tex]\[
-6 \frac{2}{3} = -6 - \frac{2}{3} = -6 - 0.6667 = -6.6667
\][/tex]
2. Convert [tex]\(-6 \frac{2}{5}\)[/tex]:
[tex]\[
-6 \frac{2}{5} = -6 - \frac{2}{5} = -6 - 0.4 = -6.4
\][/tex]
The set now consists of the following decimals:
[tex]\[
-6.6667, -6.6, -6.06, -6.4
\][/tex]
Step 2: Compare the decimal values
Let's list them in ascending order (since we are looking for the greatest number, it helps to see them organized this way):
1. [tex]\(-6.6667\)[/tex]
2. [tex]\(-6.6\)[/tex]
3. [tex]\(-6.4\)[/tex]
4. [tex]\(-6.06\)[/tex]
Clearly, [tex]\(-6.06\)[/tex] is the largest value as it is less negative than the other numbers.
Conclusion:
The greatest number in the set is [tex]\( \boxed{-6.06} \)[/tex].
