Okay. That's a question I can understand:) Whether I can answer it is a different matter, but I'll have a go.

If your numbers are in the range 0.0 to 1.0 (or possibly -1.0 to +1.0, but that being pedantic), then that number is significant. However, if your numbers get larger, in the range 1 .. 10, then the significant value is different. vis.

perl58 -le "$eps = 1; while( 10 < 10 + $eps ){ $eps /= 2 ; } print $ep
+s,"
8.88178419700125e-016
[download]

And when the number gets larger still, then it changes again.

perl58 -le "$eps = 1; while( 100 < 100 + $eps ){ $eps /= 2 }print $eps
+"
7.105427357601e-015
[download]

And, of course, it works the other way too

perl58 -le "$eps = 1; while( 0.1 < 0.1 + $eps ){ $eps /= 2 } print $ep
+s"
6.93889390390723e-018
[download]

perl58 -e "for(-15..16) { $eps=1; while( qq[1E$_] < qq[1E$_] + $eps )
           { $eps /= 2; } printf '%20.20f : %32.32f' . $/, qq[1E$_], $
+eps }"
0.00000000000000100000 : 0.00000000000000000000000000000010
0.00000000000001000000 : 0.00000000000000000000000000000039
0.00000000000010000000 : 0.00000000000000000000000000000631
0.00000000000100000000 : 0.00000000000000000000000000005049
0.00000000001000000000 : 0.00000000000000000000000000040390
0.00000000010000000000 : 0.00000000000000000000000000323117
0.00000000100000000000 : 0.00000000000000000000000005169879
0.00000001000000000000 : 0.00000000000000000000000082718061
0.00000010000000000000 : 0.00000000000000000000000661744490
0.00000100000000000000 : 0.00000000000000000000005293955920
0.00001000000000000000 : 0.00000000000000000000042351647363
0.00010000000000000000 : 0.00000000000000000000338813178902
0.00100000000000000000 : 0.00000000000000000010842021724855
0.01000000000000000000 : 0.00000000000000000043368086899420
0.10000000000000001000 : 0.00000000000000000693889390390723
1.00000000000000000000 : 0.00000000000000011102230246251565
10.00000000000000000000 : 0.00000000000000088817841970012523
100.00000000000000000000 : 0.00000000000000710542735760100190
1000.00000000000000000000 : 0.00000000000005684341886080801500
10000.00000000000000000000 : 0.00000000000090949470177292824000
100000.00000000000000000000 : 0.00000000000727595761418342590000
1000000.00000000000000000000 : 0.00000000005820766091346740700000
10000000.00000000000000000000 : 0.00000000093132257461547852000000
100000000.00000000000000000000 : 0.00000000745058059692382810000000
1000000000.00000000000000000000 : 0.00000005960464477539062500000000
10000000000.00000000000000000000 : 0.00000095367431640625000000000000
100000000000.00000000000000000000 : 0.00000762939453125000000000000000
1000000000000.00000000000000000000 : 0.0000610351562500000000000000000
+0
10000000000000.00000000000000000000 : 0.000976562500000000000000000000
+00
100000000000000.00000000000000000000 : 0.00781250000000000000000000000
+000
1000000000000000.00000000000000000000 : 0.0625000000000000000000000000
+0000
10000000000000000.00000000000000000000 : 1.000000000000000000000000000
+00000
[download]

There are three things to notice here.

1. The accuracy of perl floating point representation is not absolute in term of "accurate to 0.00000000000000001".

   It's accuracy is defined in terms of significant digits, rather than decimal places.

2. Measuring this accuracy, is problematic.

   If you look at the left-hand number for 1e-1 is shows up as 0.10000000000000001000. This is because some decimal fractions simply cannot be represented accurately using a binary fraction. 0.1 is one such, an 0.9 is another.

   perl58 -le"printf '%32.32f', 0.9"
   0.90000000000000002000000000000000
   [download]

3. Perl's floating point representation, is really the floating point representation (and accuracy) of the C compiler used to compile your version of perl.

   In turn, that accuracy is (probably) (one of the) IEEE floating point representation(s), which is the same as is used (in most cases) by your (and almost every) floating point processor. As such, you will probably get a similar level of accuracy (or inaccuracy) regardless of the language you use on your processor, unless the language uses it's own libraries to perform floating point math.

   If you need this type of accuracy, (if you were calculating the trajectories for spacecraft heading to Mars for example, or calculating the US national debt:), then perl also has Math::BigFloat libraries, which will allow you to calculate to a precision that is essentially limited only by the memory capacity of your computer. Which on an average 64 or 128MB machine is (probably) accurate enough to align your telescope to one edge of a human hair lying on the surface of Pluto (provided there are no trucks rumbling by within a thousands miles:) or to total up the number of atoms in the Earth, and our Solar System (and quite possibly all the stars we can see, but I won't guarentee that bit:). The penalty of course, is speed. If you need that kind of accuracy, you are going to have to be prepared to wait a while for your answers.

For much more (and much more accurate:) information, you might like to read IEEE reals.

In summary, perl's floats are accurate to approx 53-binary bits or approx. 16 significant (decimal) digits (not places).