Answer
The base three numeral for the provided base ten numeral is\[{{2212}_{\text{three}}}.\]
Work Step by Step
To convert base ten numeral to any other base,divide given numeral with greatest number in the power of base value as follows:
\[27\overset{2}{\overline{\left){\begin{align}
& 77 \\
& \underline{54} \\
& 23 \\
\end{align}}\right.}}\]
Divide 23 by 9:
\[9\overset{2}{\overline{\left){\begin{align}
& 23 \\
& \underline{18} \\
& \text{ }5 \\
\end{align}}\right.}}\]
Divide 5 by 3:
\[3\overset{1}{\overline{\left){\begin{align}
& 5 \\
& {\underset{\scriptscriptstyle-}{3}} \\
& 2 \\
\end{align}}\right.}}\]
Here, the base value of resultant numeral is \[3\]. So, powers of base numerals are \[{{3}^{0}},\,{{3}^{1}},\,{{3}^{2}},\,{{3}^{3}},....\]which can be written as\[1,\,\,3,\,\,9,\,\,27,....\]when solved.
Now, use the quotients of each division, base ten numeral can be found as follows:\[\begin{align}
& 2\times 27\,+2\times 9\,+1\times 3\,+2\times 1\,=2\times {{3}^{3\,}}+\,2\times {{3}^{2}}\,+1\times {{3}^{1}}\,+2\times {{3}^{0}} \\
& ={{2212}_{\text{three}}}
\end{align}\]
Hence, the base three numeral for the provided base ten numeral is\[{{2212}_{\text{three}}}.\]
