they want me to round the result to the correct number of significant figures.

The first part:
[tex]24.9\times1.99=49.551[/tex]Since the first number is 1 decimal place and second number is 2 decimals, we will round to 1 decimal.
Thus,
49.551 = 49.6
Next part of the problem becomes:
[tex]49.6\div106.19[/tex]The calculation provides the answer: 0.4670...
The first number has 3 significant figures, that's the limit because next number has 5 significant figures. So, we round off our answer to 3 significant figures (3 decimal place, in this case)
Thus, the answer is:
0.467