To order the numbers -3, -4, -1.5, and 2.7 from greatest to least based on their absolute values, follow these steps:
1. Determine the absolute values:
- [tex]\(|-3| = 3\)[/tex]
- [tex]\(|-4| = 4\)[/tex]
- [tex]\(|-1.5| = 1.5\)[/tex]
- [tex]\(|2.7| = 2.7\)[/tex]
2. Pair each number with its absolute value:
- [tex]\((-3, 3)\)[/tex]
- [tex]\((-4, 4)\)[/tex]
- [tex]\((-1.5, 1.5)\)[/tex]
- [tex]\((2.7, 2.7)\)[/tex]
3. Sort the pairs based on the absolute values in descending order (from largest to smallest absolute value):
- [tex]\((-4, 4)\)[/tex]
- [tex]\((-3, 3)\)[/tex]
- [tex]\((2.7, 2.7)\)[/tex]
- [tex]\((-1.5, 1.5)\)[/tex]
4. Extract the original numbers in the sorted order:
- [tex]\(-4\)[/tex]
- [tex]\(-3\)[/tex]
- [tex]\(2.7\)[/tex]
- [tex]\(-1.5\)[/tex]
5. Match the sorted list with the provided choices:
- A: [tex]\(|-4|>|-3|>|-1.5|>|2.7|\)[/tex] (Incorrect)
- B: [tex]\(|-1.5|>|2.7|>|-3|>|-4|\)[/tex] (Incorrect)
- C: [tex]\(|-4|>|-3|>|2.7|>|-1.5|\)[/tex] (Correct)
- D: [tex]\(|-1.5|>|-3|>|-4|>|2.7|\)[/tex] (Incorrect)
Based on the correct ordering and absolute values, the option that accurately represents [tex]\(|-4| > |-3| > |2.7| > |-1.5|\)[/tex] is correct.
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
