Sure! Let's go through the placement of each number on the number line step-by-step. We'll compare their values to understand their order:
1. [tex]\(-\frac{13}{6}\)[/tex]:
- This value is a negative fraction. Calculating it, [tex]\(-\frac{13}{6} \approx -2.1667\)[/tex].
- This is the smallest number in our list.
2. -1.62:
- This is straightforward. It is already in decimal form and it is the next smallest number after [tex]\(-\frac{13}{6}\)[/tex].
3. -1.26:
- Another negative value, but closer to zero as compared to -1.62.
4. 0.21:
- A positive decimal. This places it to the right of zero, and it is the smallest positive number in this list.
5. [tex]\(\frac{3}{11}\)[/tex]:
- Convert this fraction to a decimal, [tex]\(\frac{3}{11} \approx 0.2727\)[/tex].
- This is slightly larger than 0.21.
6. [tex]\(\frac{5}{3}\)[/tex]:
- Convert this fraction to a decimal, [tex]\(\frac{5}{3} \approx 1.6667\)[/tex].
- This is the next largest value past [tex]\(\frac{3}{11}\)[/tex].
7. 2 [tex]\(\frac{2}{9}\)[/tex]:
- Convert this mixed number to a decimal, [tex]\(2 + \frac{2}{9} \approx 2.2222\)[/tex].
- This places it just before 2.375.
8. 2.375:
- This is straightforward as it is already in decimal form and is the largest number in our list.
Placing these along the number line from smallest to largest, we get:
1. [tex]\(-\frac{13}{6}\)[/tex] (approximately -2.1667)
2. -1.62
3. -1.26
4. 0.21
5. [tex]\(\frac{3}{11}\)[/tex] (approximately 0.2727)
6. [tex]\(\frac{5}{3}\)[/tex] (approximately 1.6667)
7. [tex]\(2 \(\frac{2}{9}\)[/tex]\) (approximately 2.2222)
8. 2.375
So, the placement of each number on the number line is as follows:
[tex]\[
\begin{aligned}
&\begin{array}{|c|c||c|c|c|c|c|c|}
\hline
\text{Number} & \text{Position on Number Line} & & -1.26 & 0.21 & \frac{3}{11} & \frac{5}{3} & 2 \frac{2}{9} & 2.375 \\
\hline
-\frac{13}{6} & \text{Smallest} & -\frac{13}{6} & -1.62 & & & & & \\
-1.62 & & & & & & & & \\
-1.26 & & & & & & & & \\
0.21 & & & & & & & & \\
\frac{3}{11} & & & & & & & & \\
\frac{5}{3} & & & & & & & & \\
2 \frac{2}{9} & & & & & & & & \\
2.375 & \text{Largest} & & & & & & & \\
\hline
\end{array}
\][/tex]
