To accurately place the given numbers on a number line, we must first understand their respective values.
1. [tex]\(-\frac{3}{2}\)[/tex]: The fraction [tex]\(-\frac{3}{2}\)[/tex] can be converted into a decimal. Dividing [tex]\(3\)[/tex] by [tex]\(2\)[/tex] gives [tex]\(1.5\)[/tex], and since it's negative, [tex]\(-\frac{3}{2}\)[/tex] equals [tex]\(-1.5\)[/tex].
2. [tex]\(0.5\)[/tex]: This number is already in decimal form and is [tex]\(0.5\)[/tex].
3. [tex]\(\sqrt{9}\)[/tex]: The square root of [tex]\(9\)[/tex] is the number that, when multiplied by itself, equals [tex]\(9\)[/tex]. This number is [tex]\(3\)[/tex].
4. [tex]\(-2\)[/tex]: The number [tex]\(-2\)[/tex] is already simplified.
Now that we have their numerical values, we can list them as:
- [tex]\(-1.5\)[/tex]
- [tex]\(0.5\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(-2\)[/tex]
To place these numbers accurately on a number line, follow these steps:
1. Identify a suitable scale for the number line that includes all given numbers. Here, we need a number line that spans from at least [tex]\(-2\)[/tex] to [tex]\(3\)[/tex].
2. Mark and label the number line with appropriate intervals. For clarity, intervals of [tex]\(1\)[/tex] unit each work well. Therefore, the line should include markers for [tex]\(-2, -1, 0, 1, 2, 3\)[/tex].
3. Place the numbers on the number line according to their values.
Now let's position the numbers:
- [tex]\(-2\)[/tex] will be placed at the point marked [tex]\(-2\)[/tex].
- [tex]\(-1.5\)[/tex] lies between [tex]\(-2\)[/tex] and [tex]\(-1\)[/tex]. It is halfway between these two markers.
- [tex]\(0.5\)[/tex] lies between [tex]\(0\)[/tex] and [tex]\(1\)[/tex]. It is halfway between these two markers.
- [tex]\(3\)[/tex] will be placed at the point marked [tex]\(3\)[/tex].
Your number line should look something like this:
```
-2 -1.5 0 0.5 1 2 3
|----|----|----|----|----|----|----|
-2 -1.5 0 0.5 1 2 3
```
Each number is now correctly placed on the number line.
