And what would the purpose hold for big_string as a CHARACTER type variable?
The key here is for the OP to understand the external (formatted) versus the SAS internal NUMERIC variable value, especially when used in a calculation or derivation of some type.
Using a FORMAT statement with a numeric variable is the key here.
There are several technical papers and SAS-hosted Language Reference: Concepts documentation available on this topic at the SAS support
http://support.sas.com/ website - consider the Google advanced search argument (or use the SAS website SEARCH facility):
numeric variable precision format site:sas.com
Scott Barry
SBBWorks, Inc.