To round the number 55.89934 to three decimal places, we follow these steps:
1. Identify the digit in the third decimal place. For the number 55.89934, the third decimal place is occupied by the digit 9.
2. Look at the digit immediately to the right of the third decimal place to determine whether to round up or stay the same. In this case, the digit immediately to the right is 3.
3. If the digit to the right (3 in this case) is less than 5, the third decimal place remains the same. If it were 5 or greater, we would round up the third decimal place by adding 1 to it.
4. Because the digit to the right is 3, which is less than 5, the 9 in the third decimal place remains unchanged.
Therefore, the number 55.89934 rounded to three decimal places is 55.899.
Among the given options:
\begin{tabular}{ll}
A & 55,890 \\
B & 55.899 \\
C & 55,800 \\
D & 55,900
\end{tabular}
The correct answer is:
[tex]\[
\boxed{B \text{ } 55.899}
\][/tex]
