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Order the numbers from greatest to least based on their absolute value. [tex]$|-3|, |-4|, |-1.5|, |2.7|$[/tex]

A. [tex]$|-4| \ \textgreater \ |-3| \ \textgreater \ |-1.5| \ \textgreater \ |2.7|$[/tex]

B. [tex][tex]$|-1.5| \ \textgreater \ |2.7| \ \textgreater \ |-3| \ \textgreater \ |-4|$[/tex][/tex]

C. [tex]$|-4| \ \textgreater \ |-3| \ \textgreater \ |2.7| \ \textgreater \ |-1.5|$[/tex]

D. [tex]$|-1.5| \ \textgreater \ |-3| \ \textgreater \ |-4| \ \textgreater \ |2.7|$[/tex]



Answer :

GinnyAnswer
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]

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