To determine the order of the numbers [tex]\(\frac{4}{5}, 0.08, 72\%, \frac{5}{11}, 0.454, 45\%\)[/tex] from greatest to least, we need to convert all of these numbers into a common format for easy comparison. We'll use percentages as our common format.
1. Convert [tex]\(\frac{4}{5}\)[/tex] to a percentage:
[tex]\[
\frac{4}{5} \times 100 = 80\%
\][/tex]
2. Convert [tex]\(0.08\)[/tex] to a percentage:
[tex]\[
0.08 \times 100 = 8\%
\][/tex]
3. 72\% is already in percentage form.
4. Convert [tex]\(\frac{5}{11}\)[/tex] to a percentage:
[tex]\[
\frac{5}{11} \times 100 \approx 45.45\%
\][/tex]
5. Convert [tex]\(0.454\)[/tex] to a percentage:
[tex]\[
0.454 \times 100 = 45.4\%
\][/tex]
6. 45\% is already in percentage form.
Now, we have the following numbers in percentage form:
[tex]\[
80\%, 8\%, 72\%, 45.45\%, 45.4\%, 45\%
\][/tex]
Next, we arrange these percentages from greatest to least:
[tex]\[
80\%, 72\%, 45.45\%, 45.4\%, 45\%, 8\%
\][/tex]
Thus, the set of numbers ordered from greatest to least is:
[tex]\[
80\%, 72\%, 45.45\%, 45.4\%, 45\%, 8\%
\][/tex]
Translating these percentages back to their original forms, we have:
[tex]\[
\frac{4}{5}, 72\%, \frac{5}{11}, 0.454, 45\%, 0.08
\][/tex]
Therefore, the set of given numbers ordered from greatest to least is:
[tex]\[
\frac{4}{5}, 72\%, \frac{5}{11}, 0.454, 45\%, 0.08
\][/tex]
