This isn't necessarily the best advice, but I personally find these traversal problems really fun to solve in perl using the $_ variable. It also gives the fastest execution time.

sub recursive_mult_by_100() {
  if (!ref) { $_ *= 100 }
  elsif (ref eq 'ARRAY') { recursive_mult_by_100 for @$_ }
  elsif (ref eq 'HASH') { recursive_mult_by_100 for values %$_ }
  else { die "Unhandled data type ".ref; }
}

recursive_mult_by_100 for $deep;
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This takes advantage of the feature where Perl aliases things to $_ during a for loop, so modifying $_ modifies the underlying thing, and where ref operates on $_ by default if you don't give it a regular parameter.

I say it's not the best advice because it isn't the most readable code, nor a standard pattern that people expect. Note that the () on the function stops it from accepting parameters, which helps you avoid the mistake of calling recursive_mult_by_100($data) and getting buggy results.