Significant Digits in Measurement
Date: 08/13/2001 at 13:38:01 From: Tricia Subject: Significant digits in measurement I understand that there are rules to determine the significant digits in measurement; however, I do not comprehend the basic concept behind the use of significant digits. It seems to me that all digits are significant, especially zeros for place value. An example of my confusion would be: How can 3000 have only one significant digit (3)? or How can 0.0050 have only two significant digits (50)? Thank you for your help!
Date: 08/13/2001 at 15:34:17 From: Doctor Peterson Subject: Re: Significant digits in measurement Hi, Tricia. The basic idea is that all digits that are not there ONLY for place value purposes are significant. Suppose I built a building that rose 10 stories high, but the first two stories were just columns holding the rest up above a highway. The first two "stories" would be important, certainly; but they wouldn't really count as part of the building, because they only hold it in place, without actually containing anything useful. The building has only eight "significant stories"! Zeros used only for place value at the right of a number are mere scaffolding holding it "above" the decimal point, and don't really contain any information. It's a lot easier to talk about significant digits when you write numbers in scientific notation, which is designed to neatly separate significant digits from the size of the number, by ensuring that no extra zeros are required in order to write it. If we write 3000 as 3 * 10^3, we can see we have only one significant digit. If I write it instead as 3.000 * 10^3, it has four, because I am explicitly telling you all four digits. When I write it as 3000, you can't tell whether the 0's are there because I know they are correct, or just because I had to put them there to write the number (placeholders). You really can't say just from looking at the number what I meant. Similarly, if we write 5.0 * 10^-3, we clearly have two significant digits. In this case, that is just as clear from 0.0050, because you know the zeros before the 5 are there only as placeholders. If those digits were non-zero, I would have had to write their correct values, whereas if the zeros in 3000 were really non-zero, I have the option of writing them or rounding them off. Scientific notation eliminates the need to write any digits as mere placeholders, so all the digits you see are significant (unless you write unnecessary zeros on the left, which would be silly). Here are several answers in our archives that are relevant to this question: Significant Figures and Scientific Notation http://mathforum.org/library/drmath/view/56291.html Rules for Significant Figures and Decimal Places http://mathforum.org/library/drmath/view/58335.html Significant Digits http://mathforum.org/library/drmath/view/57160.html I searched the archives (http://mathforum.org/mathgrepform.html ) for "significant digits" to find them. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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