Let's break down the problem step-by-step and convert each of the given numbers into decimal form. Then, we will determine their order from smallest to largest.
Given numbers:
1. [tex]\(\sqrt{3}\)[/tex]
2. [tex]\(-\frac{2}{3}\)[/tex]
3. [tex]\(-2\)[/tex]
### Step-by-Step Solution
1. Convert each number to its decimal form:
- Number 1: [tex]\(\sqrt{3}\)[/tex]
[tex]\[
\sqrt{3} \approx 1.7320508075688772
\][/tex]
- Number 2: [tex]\(-\frac{2}{3}\)[/tex]
[tex]\[
-\frac{2}{3} \approx -0.6666666666666666
\][/tex]
- Number 3: [tex]\(-2\)[/tex]
[tex]\[
-2 = -2.0
\][/tex]
Now we have the decimal forms:
- [tex]\(\sqrt{3} \approx 1.7320508075688772\)[/tex]
- [tex]\(-\frac{2}{3} \approx -0.6666666666666666\)[/tex]
- [tex]\(-2 = -2.0\)[/tex]
2. Determine their order from smallest to largest:
To sort the numbers, compare their decimal forms.
- [tex]\(-2.0\)[/tex]
- [tex]\(-0.6666666666666666\)[/tex]
- [tex]\(1.7320508075688772\)[/tex]
Arranging these decimals from smallest to largest:
[tex]\[
-2.0, -0.6666666666666666, 1.7320508075688772
\][/tex]
### Final Answer
The order of the numbers from smallest to largest is:
[tex]\[
-2 \quad \square \quad -\frac{2}{3} \quad \square \quad \sqrt{3}
\][/tex]
In decimal form:
[tex]\[
-2.0, -0.6666666666666666, 1.7320508075688772
\][/tex]
This provides a clear understanding of the conversion and sorting process for the given numbers.
