To determine which of the numbers in the set [tex]\(-6 \frac{2}{3}, -6.6, -6.06, -6 \frac{2}{5}\)[/tex] is the greatest, let's first convert the given fractional numbers to their decimal forms so that we can make a direct comparison among all the numbers.
1. Convert [tex]\( -6 \frac{2}{3} \)[/tex] to decimal:
[tex]\[
-6 \frac{2}{3} = -6 - \frac{2}{3} = -6 - 0.666666666666667 = -6.666666666666667
\][/tex]
2. Compare [tex]\(-6.6\)[/tex] as it is already in decimal form:
[tex]\[
-6.6 = -6.6
\][/tex]
3. Compare [tex]\(-6.06\)[/tex] as it is already in decimal form:
[tex]\[
-6.06 = -6.06
\][/tex]
4. Convert [tex]\( -6 \frac{2}{5} \)[/tex] to decimal:
[tex]\[
-6 \frac{2}{5} = -6 - \frac{2}{5} = -6 - 0.4 = -6.4
\][/tex]
Now we have all the numbers in decimal form:
[tex]\[
-6.666666666666667, -6.6, -6.06, -6.4
\][/tex]
Next, let's compare these decimal numbers to determine which is the greatest. Remember that in the context of negative numbers, the greatest number is the one that is the least negative (closest to zero).
List of numbers in descending order:
[tex]\[
-6.666666666666667, -6.6, -6.4, -6.06
\][/tex]
By comparing:
- [tex]\(-6.666666666666667\)[/tex] is less than [tex]\(-6.6\)[/tex]
- [tex]\(-6.6\)[/tex] is less than [tex]\(-6.4\)[/tex]
- [tex]\(-6.4\)[/tex] is less than [tex]\(-6.06\)[/tex]
Hence, the least negative (or the greatest) number among them is:
[tex]\[
-6.06
\][/tex]
Therefore, the greatest number in the given set is:
[tex]\[
\boxed{-6.06}
\][/tex]
