To determine which of the following lists the numbers in decreasing order:
[tex]\(-4, 0.4, \frac{41}{5}, -0.04\)[/tex], we need to compare the values and arrange them from the largest to the smallest. Let's examine the values:
1. Convert fractions and decimals to comparable forms:
- [tex]\(\frac{41}{5}\)[/tex] can be converted to [tex]\(\frac{41}{5} = 8.2\)[/tex]
- [tex]\(0.4\)[/tex] is already a decimal and is [tex]\(0.4\)[/tex]
- [tex]\(-0.04\)[/tex] is already a decimal and is [tex]\(-0.04\)[/tex]
- [tex]\(-4\)[/tex] is already an integer, and so remains [tex]\(-4\)[/tex]
2. Compare the values to arrange in decreasing order:
- The largest value here is [tex]\(8.2\)[/tex]
- Next, the second largest value is [tex]\(0.4\)[/tex]
- Moving to the smaller side, [tex]\(-0.04\)[/tex] is greater than [tex]\(-4\)[/tex]
- Lastly, the smallest value is [tex]\(-4\)[/tex]
3. Arrange the values in decreasing order:
- From the largest to the smallest, the order is: [tex]\(8.2\)[/tex], [tex]\(0.4\)[/tex], [tex]\(-0.04\)[/tex], [tex]\(-4\)[/tex]
4. Match this order with the given options:
- Option A: [tex]\(-4, 0.4, \frac{41}{5}, -0.04\)[/tex]
- Option B: [tex]\(-0.04, -4, 0.4, \frac{41}{5}\)[/tex]
- Option C: [tex]\(\frac{41}{5}, 0.4, -4, -0.04\)[/tex]
- Option D: [tex]\(\frac{41}{5}, 0.4, -0.04, -4\)[/tex]
Now looking at the options, Option D [tex]\(\left( \frac{41}{5}, 0.4, -0.04, -4 \right)\)[/tex] matches the order we established perfectly.
Therefore, the correct answer is [tex]\(\boxed{D}\)[/tex].
