#### Answer

$0.115150$

#### Work Step by Step

To multiply the two numbers, the decimals can be initially ignored to obtain $4606 \times 25$.
Multiply the numbers to obtain:
\begin{array}{ccc}
&&\space \text{ }4606
\\&\times &\underline{\space \text{ } \space \text{ }\space \text{ } \space25}
\\&&23030
\\&&\underline{\space 9212\space \text{ } \space}
\\&&115150\end{array}
The first factor has 3 decimals places and the second factor has $3$ decimal places.
Thus, the product has $3+3=6$ decimal places.
Therefore, the product is $0.115150$.