Let's solve this problem step-by-step.
### Fraction: [tex]\(\frac{4}{9}\)[/tex]
1. Decimal to One Place:
- The decimal approximation of [tex]\(\frac{4}{9}\)[/tex] rounded to one decimal place is 0.4.
2. Decimal to Two Places:
- The decimal approximation of [tex]\(\frac{4}{9}\)[/tex] rounded to two decimal places is 0.44.
3. Decimal to Three Places:
- The decimal approximation of [tex]\(\frac{4}{9}\)[/tex] rounded to three decimal places is 0.444.
### Fraction: [tex]\(\frac{4}{13}\)[/tex]
1. Decimal to One Place:
- The decimal approximation of [tex]\(\frac{4}{13}\)[/tex] rounded to one decimal place is 0.3.
2. Decimal to Two Places:
- The decimal approximation of [tex]\(\frac{4}{13}\)[/tex] rounded to two decimal places is 0.31.
3. Decimal to Three Places:
- The decimal approximation of [tex]\(\frac{4}{13}\)[/tex] rounded to three decimal places is 0.308.
### Fraction: [tex]\(\frac{7}{24}\)[/tex]
1. Decimal to One Place:
- The decimal approximation of [tex]\(\frac{7}{24}\)[/tex] rounded to one decimal place is 0.3.
2. Decimal to Two Places:
- The decimal approximation of [tex]\(\frac{7}{24}\)[/tex] rounded to two decimal places is 0.29.
3. Decimal to Three Places:
- The decimal approximation of [tex]\(\frac{7}{24}\)[/tex] rounded to three decimal places is 0.292.
### Final Table
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{4}{|c|}{ Write the Approximating Fractions with Repeating Decimals } \\
\hline \multicolumn{4}{|c|}{\begin{tabular}{l}
Write the fractions using decimal approximations. \\
The example in the first row will guide you on how to enter your answers.
\end{tabular}} \\
\hline Fraction & \begin{tabular}{l}
Decimal to One Place \\
Value
\end{tabular} & \begin{tabular}{l}
Decimal to Two Place \\
Values
\end{tabular} & \begin{tabular}{l}
Decimal to Three Place \\
Values
\end{tabular} \\
\hline \begin{tabular}{l}
$\frac{1}{3}$
\end{tabular} & 0.3 & 0.33 & 0.333 \\
\hline \begin{tabular}{l}
$\frac{4}{9}$
\end{tabular} & 0.4 & 0.44 & 0.444 \\
\hline \begin{tabular}{l}
$\frac{4}{13}$
\end{tabular} & 0.3 & 0.31 & 0.308 \\
\hline \begin{tabular}{l}
$\frac{7}{24}$
\end{tabular} & 0.3 & 0.29 & 0.292 \\
\hline
\end{tabular}
\][/tex]
This table provides the decimal approximations of the given fractions to one, two, and three decimal places.
