       Re: Why?

• To: mathgroup at smc.vnet.net
• Subject: [mg110010] Re: Why?
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Fri, 28 May 2010 07:23:42 -0400 (EDT)

```On 5/27/10 at 6:46 AM, lehin.p at gmail.com (Alexey) wrote:

>In:= N[1.000000000000000000000001 - 1, 60]

>Out= 0.*10^-24

>I can not understand why this happens. Can anyone explain the
>reason? What is about "arbitrary precision arithmetics"?

The problem is you are attempting to convert a number from one
precision to a higher precision. That is:

In:= Precision[1.000000000000000000000001]

Out= 24.

But if you had entered the real value as having 60 digit
precision things would work as you expect. That is:

In:= 1.000000000000000000000001`60 - 1

Out= 1.00000000000000000000000000000000000*10^-24

or you could have started with exact values and used N to
convert then to 60 digit precision, i.e.,

In:= N[1 + 10^-24, 60] - 1

Out= 1.00000000000000000000000000000000000*10^-24

```

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