Land surveyors for ordinary property surveys work to 8 decimal places. 
Geodetic surveyors (say across a state or country) work to many more. In 
1960 surveying class, a required text was logarithms of the trig 
functions (sine, cosine, tangent, and cotangent) to 8 places. Slide rule 
couldn't be used, and a few rotary calculators were available. We did 
use hand operated rotary calculators ,where one had to manually shift 
the carriage to do the carry, or underflow in division. The University 
computer was an IBM 650 with many tubes (valves).  If you go to your 
state's site for land surveyor registration, you should find the 
accuracy that surveyors are bound to in the regulations.

Alan B. Pearce wrote:
>>>  I'm looking forwards to the day when they discover the point beyond
>>>    which all subsequent digits of Pi are zero :-)
>>>       
>> Already here.  The point at which that happens, however, depends on the
>> accuracy you can measure with.  If your limit is measuring one cycle of
>> earth's orbit to within 1mm, then the zeros start at the 16th digit past
>> the decimal point.  In other words Pi =
>> 3.1415926535897930000000000000000000000000000...  And even if I'm wrong,
>> the point is you can't tell.
>>     
>
> I believe that 5 decimal places is enough to calculate the circumference of 
> the earth to within a handspan. Sorry don't have a reference, I just 
> remember being told it at one stage. 
>
>   
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