$hash{ sprintf '%.6e', $number };

##</code><code>##

printf "%20s becomes %.6e\n", $_, $_ for map{ 
    ( $_, ( $_ + 1e-10 ) ) 
} map{ 
    "2e$_" 
} -300, -30, -3, 0, 3, 30, 300;

              2e-300 becomes 2.000000e-300
              1e-010 becomes 1.000000e-010
               2e-30 becomes 2.000000e-030
              1e-010 becomes 1.000000e-010
                2e-3 becomes 2.000000e-003
        0.0020000001 becomes 2.000000e-003
                 2e0 becomes 2.000000e+000
        2.0000000001 becomes 2.000000e+000
                 2e3 becomes 2.000000e+003
     2000.0000000001 becomes 2.000000e+003
                2e30 becomes 2.000000e+030
              2e+030 becomes 2.000000e+030
               2e300 becomes 2.000000e+300
              2e+300 becomes 2.000000e+300

printf "%20s becomes %.11e\n", $_, $_ for map{ 
     ( $_, ( $_ + 1e-10 ) ) 
} map{ 
    "2e$_" 
} -300, -30, -3, 0, 3, 30, 30

              2e-300 becomes 2.00000000000e-300
              1e-010 becomes 1.00000000000e-010
               2e-30 becomes 2.00000000000e-030
              1e-010 becomes 1.00000000000e-010
                2e-3 becomes 2.00000000000e-003
        0.0020000001 becomes 2.00000010000e-003
                 2e0 becomes 2.00000000000e+000
        2.0000000001 becomes 2.00000000010e+000
                 2e3 becomes 2.00000000000e+003
     2000.0000000001 becomes 2.00000000000e+003
                2e30 becomes 2.00000000000e+030
              2e+030 becomes 2.00000000000e+030
               2e300 becomes 2.00000000000e+300
              2e+300 becomes 2.00000000000e+300