Sure, let's complete the table step-by-step.
1. For the fraction [tex]\(\frac{1}{2}\)[/tex]:
- Fraction: [tex]\(\frac{1}{2}\)[/tex]
- Percentage: A fraction of [tex]\(\frac{1}{2}\)[/tex] is equivalent to 50% when converted to a percentage.
[tex]\(\frac{1}{2} \times 100 = 50\%\)[/tex]
- Decimal: A fraction of [tex]\(\frac{1}{2}\)[/tex] converts to a decimal of 0.5.
2. For the percentage [tex]\(66.\dot{6} \%\)[/tex]:
- Percentage: [tex]\(66.\dot{6}\%\)[/tex]
- Fraction: [tex]\(66.\dot{6}\%\)[/tex] as a fraction can be represented as the repeating decimal [tex]\(0.\dot{6}\)[/tex] which is [tex]\(\frac{2}{3}\)[/tex] in fraction form.
3. For the decimal [tex]\(0.\dot{6}\)[/tex]:
- Decimal: [tex]\(0.\dot{6}\)[/tex]
- Fraction: As noted above, [tex]\(0.\dot{6}\)[/tex] repeats and is equivalent to the fraction [tex]\(\frac{2}{3}\)[/tex].
4. Completing the table:
[tex]\[
\begin{array}{c|c|c}
\text{Fraction} & \text{Percentage} & \text{Decimal} \\
\hline
\frac{1}{5} & 20\% & 0.2 \\
\hline
\frac{1}{4} & 25\% & 0.25 \\
\hline
\frac{1}{2} & 50\% & 0.5 \\
\hline
\frac{2}{3} & 66.\dot{6}\% & 0.\dot{6} \\
\end{array}
\][/tex]
Therefore, the completed table is:
[tex]\[
\begin{array}{c|c|c}
\text{Fraction} & \text{Percentage} & \text{Decimal} \\
\hline
\frac{1}{5} & 20\% & 0.2 \\
\hline
\frac{1}{4} & 25\% & 0.25 \\
\hline
\frac{1}{2} & 50\% & 0.5 \\
\hline
\frac{2}{3} & 66.\dot{6}\% & 0.\dot{6} \\
\end{array}
\][/tex]
