Answer
Base five Numeral is \[{{1232}_{\text{five}}}\]
Work Step by Step
Let’s convert by Using Roman Numeral System,
First write the given Roman numeral as Hindu Arabian Numeral
CXCII\[\,=100+\left( 100-10 \right)+2=192\]
Now, let’s find out the base five numeral using base ten Hindu Arabic numeral,
The Place values in base five numeral are \[{{5}^{1}},\,{{5}^{2}},{{5}^{3}},{{5}^{4}},\ldots \] or \[5,25,125,625,\ldots \]
Using highest divisor from these place values which is less than dividend for the first time and then continue in same manner, we get
\[\begin{align}
192=125\overset{1}{\overline{\left){192}\right.}} & \\
\text{ }\underline{125} & \\
\text{ 67} & \\
\end{align}\]
Then,
\[\begin{align}
& 25\overset{2}{\overline{\left){67}\right.}} \\
& \text{ }\underline{50} \\
& \text{ 17} \\
\end{align}\]
Then,
\[\begin{align}
& 5\overset{3}{\overline{\left){17}\right.}} \\
& \text{ }\underline{15} \\
& \text{ }2 \\
\end{align}\]
So,
${{192}_{\text{ten}}}={{1232}_{\text{five}}}$
Using the three quotients and the last remainder, we can directly write the Base five Numeral as above.
