       Accuracy question

• To: mathgroup at smc.vnet.net
• Subject: [mg14030] Accuracy question
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Wed, 16 Sep 1998 14:12:09 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```In the lines below SetPrecision[Round,False] makes it so Precision and
accuracy return the actual floating point numbers that are used
internally. \$NumberMarks=True, makes it so (among other things)
InputForm[num] returns all digits used internally, and the precision
marks at the end of inexact numbers.

In:=
SetPrecision[Round,False];
\$NumberMarks=True;
x=12345.67;

Out shows exactly how Precision[x] is represented internally.  Out
shows that Precision[x] is the number closest to  Log[10, 2^53].

In:=
Precision[x]//InputForm

Out=
15.9545897701910028`

In:=
N[N[Log[10,2^53],17]]//InputForm

Out=
15.9545897701910028`

The next line shows exactly how Accuracy[x] is represented internally.
Where does this number come from?
Since accuracy is the number of digits to the right of the decimal I
expect to get roughly 11.9.  But why
( 11.8630751061039617` )?

In:=
Accuracy[x]//InputForm

Out=
11.8630751061039617`

______________________________
Cheers,
Ted Ersek

```

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