Significant Digits

Date: 09/07/98 at 14:44:02
From: Bradley Casey
Subject: Physics Math

What are significant digits?

Date: 09/08/98 at 15:17:16
From: Doctor Mitteldorf
Subject: Re: Physics Math

Dear Bradley,

Whenever you make a measurement, the measurement isn't precise.  
Scientists like to compare their experiments with a theory, and the 
measurement never agrees completely with the theory. But if the 
difference between the measurement and the theory is small, maybe the 
theory can still be right, and the error in the measurement accounts 
for the mismatch. This is the reason scientists are always thinking 
about error estimates when they make a measurement.  

Say you measure the length of your classroom with a meterstick. You 
line up the meterstick and do it by eye, and you get 10.31425 meters.  
That last 25 represents a quarter of a millimeter.

When you think about the size of the error you could have made, you 
have to admit that you could be as much as 5 millimeters off. After 
all, the line you measured on might not have been exactly straight; 
the room isn't completely square, you eyeballed the ruler when you 
placed it end to end...

So you could say your measurement is 10.31425 meters with an 
uncertainty of .005 meters. It could be as much as 10.319 or as little 
as 10.309. That means that the 10.31 are the 4 significant digits; the 
fifth digit, the 4, is only slightly significant (since it could be as 
much as a 9) and the remaining digits aren't significant at all, and 
should be dropped, by convention, when you report your result. The 2 
and the 5 don't really have any experimental meaning; they are not 
significant digits. The 4 is optional in this case.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/