First, remove the decimal points. We come back to this later.
6355
×711
6355
63550
4448500
4518405
Now we have to put in the decimal point. Count the number of digits after the decimal point for each of the two numbers: 63.55 has 2 and 7.11 also has 2, 2+2=4 so we need to put the decimal point 4 places from the end of the product: 451.8405.