SSIS HOW TO CONVERT VARCHAR "null" TO FLOAT null

Here is the problem:

I' reading a flat file (csv) which have some columns with float values like 12.1 or 0.345
The target is a column type float on a SQL Server table
Using (DT_R8)MyColumn all values are correcly converted into float except for some that have the text "NULL" which are converte to float vaule 0.

Question:
How do I make these specific values to be converted to real database NULL instead?