Significant Digits and Irrational Numbers
Date: 09/24/2005 at 22:20:25 From: Alex Subject: How do you determine the signifigant digits of irrationals Dear Dr. Math, How can you determine the signifigant digits of a non-terminating or irrational number like pi? I know the rules for finding signifigant digits of an answer, but what if your answer doesn't terminate? How do you express the signifigant digits?
Date: 09/24/2005 at 23:05:46 From: Doctor Peterson Subject: Re: How do you determine the signifigant digits of irrationals Hi, Alex. Any exact number (not a measurement, but a known number such as pi or sqrt(2)) is considered to have infinitely many significant digits, in itself, since there is no limit to the number of digits we COULD know. However, in a specific calculation, we can only use some approximation to it, which means using some chosen number of significant digits, which will restrict our accuracy. The proper thing to do, then, is to be sure to use at least enough sigdigs in your calculation that it will not affect the accuracy of the result. For example, if you are finding the area of a circle using a radius given as 1.23 meters, you would want to use at least three digits of pi, say 3.14 or 3.142. Most likely, these days, you would just use the full accuracy of the constant built into your calculator, and not have to worry! Effectively, then, you have infinitely many sigdigs and can ignore it. You mention your answer. You always determine the number of sigdigs there not from what the answer looks like itself, but from the sigdigs in the given numbers, and then round your answer appropriately. So it doesn't matter whether the answer you calculate terminates or not--you MAKE it terminate at the appropriate place! See this page for other aspects: Significant Figures/Digits http://mathforum.org/library/drmath/sets/select/dm_sig_digits.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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