Like this?

#!/usr/bin/env perl
use 5.010; use strict; use warnings;

sub normalize {
    my $n = shift;      # start with $n between .01 and 8000 inclusive
    return( 
      ($n - .01)        # shift range to begin at 0
      / 7999.99         # divide by original range
      * 9               # multiply by new range
      + 1);             # shift up to new start of 1
}

say "$_ : ". normalize($_) for (.01, 1, 3000, 8000);
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