To determine the greatest number in the given set [tex]\(-6 \frac{2}{3}, -6.6, -6.06, -6 \frac{2}{5}\)[/tex], we need to convert all the mixed fractions to decimal form and then compare them.
1. Convert the mixed fractions to decimals:
- For [tex]\(-6 \frac{2}{3}\)[/tex]:
[tex]\[
-6 \frac{2}{3} = -6 - \frac{2}{3} = -6 - 0.666666... \approx -6.666666666666667
\][/tex]
- For [tex]\(-6 \frac{2}{5}\)[/tex]:
[tex]\[
-6 \frac{2}{5} = -6 - \frac{2}{5} = -6 - 0.4 = -6.4
\][/tex]
2. Now, we have the following set of decimal numbers:
[tex]\[
\{-6.666666666666667, -6.6, -6.06, -6.4\}
\][/tex]
3. Compare these decimal values to determine the greatest:
- [tex]\(-6.666666666666667\)[/tex]
- [tex]\(-6.6\)[/tex]
- [tex]\(-6.06\)[/tex]
- [tex]\(-6.4\)[/tex]
Notice that the greatest number is the one that is least negative.
Comparison:
- [tex]\(-6.06\)[/tex] is the least negative number compared to the others.
Therefore, the greatest number in the given set is:
[tex]\[ \boxed{-6.06} \][/tex]
Thus, the answer to the question is(c) -6.06.
