Let's classify each number as either rational or irrational based on their numerical values and properties:
1. [tex]\(\3 \cdot \sqrt{25}\)[/tex]
- Calculating [tex]\(\sqrt{25}\)[/tex] gives 5, and multiplying by 3 gives 15. Since 15 is a terminating decimal, it is a rational number.
2. [tex]\(-\frac{11}{151}\)[/tex]
- This is a fraction representing a quotient of two integers. Though it's a small number, it is indeed a rational number as the division of two integers (where the denominator is not zero) is always rational.
3. [tex]\(1.1625\)[/tex]
- [tex]\(1.1625\)[/tex] is given as a rational number because it is a terminating decimal.
4. [tex]\(5.15603418923 \ldots\)[/tex]
- This number appears to be a non-repeating, non-terminating decimal, which is indicative of an irrational number.
5. [tex]\(\sqrt{256}\)[/tex]
- Calculating [tex]\(\sqrt{256}\)[/tex] gives 16, which is a whole number. Thus, it is a rational number.
6. [tex]\(\sqrt{141}\)[/tex]
- The square root of 141 is not a perfect square, which results in an irrational number.
Now we can classify these numbers correctly in the table:
[tex]\[
\begin{tabular}{|l|l|}
\hline
\text{Rational Numbers} & \text{Irrational Numbers} \\
\hline
15.0 & 11.874342087037917 \\
-0.0728476821192053 & \\
1.1625 & \\
5.15603418923 & \\
16.0 & \\
\hline
\end{tabular}
\][/tex]
Hence, filling the table with the numbers classified:
[tex]\[
\begin{tabular}{|l|l|}
\hline
\text{Rational Numbers} & \text{Irrational Numbers} \\
\hline
15.0 & 11.874342087037917 \\
-0.0728476821192053 & \\
1.1625 & \\
5.15603418923 & \\
16.0 & \\
\hline
\end{tabular}
\][/tex]
The rational numbers are [tex]\(15.0\)[/tex], [tex]\(-0.0728476821192053\)[/tex], [tex]\(1.1625\)[/tex], [tex]\(5.15603418923\)[/tex], and [tex]\(16.0\)[/tex]. The irrational number is [tex]\(11.874342087037917\)[/tex].
