To solve the problem of ordering the numbers [tex]\( 9.42479, \sqrt{80}, 3\pi, 9 \frac{2}{5}, \text{and} 9.4248 \)[/tex] from least to greatest, we need to convert all these numbers to their decimal forms and then compare them.
1. [tex]\( 9.42479 \)[/tex] is already in decimal form.
2. [tex]\( \sqrt{80} \)[/tex] is approximately [tex]\( 8.94427 \)[/tex].
3. [tex]\( 3\pi \)[/tex] is approximately [tex]\( 9.42477796 \)[/tex].
4. [tex]\( 9 \frac{2}{5} \)[/tex] can be converted to a decimal as follows:
[tex]\[
9 + \frac{2}{5} = 9 + 0.4 = 9.4
\][/tex]
5. [tex]\( 9.4248 \)[/tex] is also already in decimal form.
So the list of numbers in their decimal forms are:
[tex]\[
9.42479, 8.94427, 9.42477796, 9.4, 9.4248
\][/tex]
Now to sort these numbers from least to greatest:
1. [tex]\( 8.94427 \)[/tex]
2. [tex]\( 9.4 \)[/tex]
3. [tex]\( 9.42477796 \)[/tex]
4. [tex]\( 9.42479 \)[/tex]
5. [tex]\( 9.4248 \)[/tex]
Thus, the sorted order is:
[tex]\[
\sqrt{80} (8.94427), 9 \frac{2}{5} (9.4), 3 \pi (9.42477796), 9.42479, 9.4248
\][/tex]
Comparing this with the provided answer choices:
1. [tex]\(\sqrt{80}, 3 \pi, 9 \frac{2}{5}, 9.42479,9.4248\)[/tex]
2. [tex]\(\sqrt{80}, 9 \frac{2}{5}, 3 \pi, 9.42479,9.4248\)[/tex]
3. [tex]\(9.4248, 9.42479, 3 \pi, 9 \frac{2}{5}, \sqrt{80}\)[/tex]
4. [tex]\(9.42479, \sqrt{80}, 3 \pi, 9 \frac{2}{5}, 9.4248\)[/tex]
The correct answer is the second one:
[tex]\[
\sqrt{80}, 9 \frac{2}{5}, 3 \pi, 9.42479, 9.4248
\][/tex]
