If you use the pack 'd', $value; approach you will likely end up with every key in your hash having a value of 1. Even a single bit difference in the lowest significant bit will prevent 2.0 & 2.000000000000000001 being considered the same.

Your best bet might be to use sprintf to truncate and stringify the values into a standardised format to whatever precision fits with your needs. Eg.

$hash{ sprintf '%.6e', $number };
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This will rationalise the continuous range of inputs into a set of discrete bands to whichever precision you need. This shows the effect of using 6 and 11 digits of precision on a range of pairs of values that have a small difference between them as input (and would be different keys using pack 'd'):

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
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