$ perl -E " { use bigrat; say 1/3+1/4; }; say 1/3+1/4; "
7/12
0.583333333333333
[download]

perl5db.pl uses eval to execute code you type, and each eval is a new lexical scope

This is one reason I don't deal with debuggers

update: oh look, someone ran into this limitation before, see Debugger, use strict, use warnings and Are debuggers good?

One idea, how to make lexical pragma global, hints ( pl_hints $^H %^H ), taint::all, but I kind of think any debugger shouldn't need help with this kind of stuff anyway, it should be a feature , but like I said, I don't use them

How can one activate bigrat in the debugger's scope?

I don't know, I never use the debugger (or debuggers). I imagine it might involve editing perl5db.pl or something else, maybe http://search.cpan.org/perldoc/perl5db.pl#DEBUGGER_STARTUP, see perldebug, perldebtut, perldebguts, or alternative debuggers like ebug