Let's start by examining the given set of numbers: [tex]\(-\frac{3}{2}\)[/tex], [tex]\(0.5\)[/tex], [tex]\(\sqrt{9}\)[/tex], and [tex]\(-2\)[/tex].
1. Identify the numerical values:
- [tex]\(-\frac{3}{2}\)[/tex] is [tex]\(-1.5\)[/tex].
- [tex]\(0.5\)[/tex] does not need conversion as it is already in decimal form.
- [tex]\(\sqrt{9}\)[/tex] is the square root of 9, which is [tex]\(3\)[/tex].
- [tex]\(-2\)[/tex] is already in its numerical form.
2. Write down the values:
- [tex]\(-1.5\)[/tex]
- [tex]\(0.5\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(-2\)[/tex]
3. Order these numbers by comparing their values to determine their positions on the number line:
- The smallest value is [tex]\(-2\)[/tex].
- Next, we have [tex]\(-1.5\)[/tex].
- After that, we have [tex]\(0.5\)[/tex].
- The largest value is [tex]\(3\)[/tex].
4. Place them in ascending order on the number line:
- [tex]\(-2\)[/tex]
- [tex]\(-1.5\)[/tex]
- [tex]\(0.5\)[/tex]
- [tex]\(3\)[/tex]
Final ordered sequence on the number line:
[tex]\[
-2, -1.5, 0.5, 3
\][/tex]
This sequence correctly orders the numbers from the smallest to the largest.
