What is a Significant Digit?Date: 12/25/2001 at 21:00:53 From: Yin Subject: Significant digits I came across a question asking for an answer with no more than "2 significant digits." My answer was 236. Should the approximate answer be 240 (rounded to the tens) or 2.4 x 10^2? And can you please explain what a significant digit is? Thank you, Yin Date: 12/26/2001 at 12:27:08 From: Doctor Rob Subject: Re: Significant digits Thanks for writing to Ask Dr. Math, Yin. The approximate answer could be either 240 or 2.4*10^2, which are (of course) equal. Significant digits arise out of inexact measurements. Suppose you measure the circumference of a circle and find that it is 90 meters long. Your measuring device is only accurate enough to tell you that the actual circumference is between 85 and 95 meters, so that the actual value, rounded to the 10's digit, is 90 meters. Then the formula tells you that the circle has a diameter of 90/Pi = 90/3.14159265... = 28.6478898... meters. Actually all you can conclude is that the diameter is between 85/Pi = 27.0563404... meters and 95/Pi = 30.2394392... meters. That means that it is silly to say that the length is 28.6478898... meters, because this implies a level of accuracy in measurement that simply doesn't exist. It would be just as reasonable to say that the length is 27.824739248234, or 29.3, or 29, or 30 meters. The best you can say is that the diameter is about 30 meters, since both bounding numbers round off to that number when rounded to the same number of decimal digits. That number of decimal digits (one in this case) is the number of significant figures in the answer. A rough rule of thumb is that the number of significant figures in an answer is about the same as the number of significant figures in the least accurate of the input data values. In the above problem, there was one significant figure in the circumference, so there should be about one significant figure in the diameter (and there was). Feel free to write again if I can help further. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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