could you explain how the following determines the
approximate
number of digits in !200e6?

a few examples:

maybe !10e2, !10e4 and !100e6

----- Original Message Follows -----
From: "John Randall" <[email protected]>
To: "Programming forum" <[email protected]>
Subject: Re: [Jprogramming] Two hundred million factorial
Date: Mon, 15 Jun 2009 16:43:59 -0400

>Dan Bron wrote:
>> How can I estimate the number of digits in   !200e6  ?
>
>Try Stirling's approximation.
>
>stirling=:(* ^.)-]
>log10=:(^. 10) %~ stirling
>
>   10^. !200x
>374.897
>   log10 200
>373.347
>   log10 200e6
>1.57335e9
>
>Best wishes,
>
>John
>
>
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