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use bignum;

...
    $c++;
    print "[$c] x= $x (".sprintf("%20.40f",$x).") \n";
}

[1] x= 0 (0.0000000000000000000000000000000000000000)
[2] x= 0.05 (0.0500000000000000027755575615628913510591)
...
[75] x= 3.7 (3.7000000000000001776356839400250464677811)
[76] x= 3.75 (3.7500000000000000000000000000000000000000)
[77] x= 3.8 (3.7999999999999998223643160599749535322189)

[78] x= 3.85 (3.8500000000000000888178419700125232338905)
[79] x= 3.9 (3.8999999999999999111821580299874767661095)
[80] x= 3.95 (3.9500000000000001776356839400250464677811)
[81] x= 4 (4.0000000000000000000000000000000000000000)