To place these numbers along the number line, we need to first interpret any fractions as decimal values and then order the numbers from the smallest to the largest. Here is the step-by-step placement of each number:
1. Convert any fractions or mixed numbers to decimals:
- 0.21 remains as 0.21.
- [tex]\(\frac{3}{11}\)[/tex] is approximately 0.2727.
- [tex]\(-\frac{13}{6}\)[/tex] is approximately -2.1667.
- 2.375 remains as 2.375.
- -1.62 remains as -1.62.
- [tex]\(2 \frac{2}{9}\)[/tex] is the same as [tex]\(2 + \frac{2}{9}\)[/tex], which is approximately 2.2222.
- [tex]\(\frac{5}{3}\)[/tex] is approximately 1.6667.
- -1.26 remains as -1.26.
2. List the decimal values:
- 0.21
- 0.2727
- -2.1667
- 2.375
- -1.62
- 2.2222
- 1.6667
- -1.26
3. Order these numbers from smallest to largest:
- -2.1667
- -1.62
- -1.26
- 0.21
- 0.2727
- 1.6667
- 2.2222
- 2.375
4. Place each number in the appropriate box along the number line:
[tex]\[
\begin{array}{|c|c|}
\hline
-2.1667 & -1.62 \\
\hline
-1.26 & 0.21 \\
\hline
0.2727 & 1.6667 \\
\hline
2.2222 & 2.375 \\
\hline
\end{array}
\][/tex]
Thus, we accurately place each number along the number line by converting all fractions to decimals and arranging them in ascending order.
