Significant Digits and Zero
Date: 05/19/99 at 16:47:37 From: Gale Carroll Subject: Significant digits What is the best way to explain significant digits? When are zeros significant and when are they not significant? What is the meaning of significant in regard to this concept? Certainly the zeros in the number 5,000 are important, but apparently not significant. How about 508? How about 23.0? How about 0.05? How about 46.50?
Date: 05/20/99 at 09:21:12 From: Doctor Peterson Subject: Re: Significant digits Hi, Gale. I'm always happy to help a teacher. A digit is significant if it contributes to the value of the number. Since zeroes on the left (if they are to the left of the decimal point) can be dropped without affecting the number, they are insignificant. Zeroes on the right (if they are to the right of the decimal point) are considered significant because they tell you that that digit is not some non-zero value, as do zeroes between digits. Zeroes between the decimal point and non-zero digits, however, are present only to keep the other digits in the right place, and are not significant - they're certainly important to the number, but are there only as a scaffolding, not as part of the building. In the case of a number like 5000, the zeroes are really ambiguous, since they might be there for either reason; when we pay attention to significant digits, we usually write numbers in scientific notation so that we don't have to write any zeroes in that position, and can avoid the ambiguity. On the other hand, if you wrote 5000.0, we would assume all the digits were significant, since decimal places are included that aren't just required to show place value. If you write 5000., it is generally taken to mean that all the zeroes are significant. In your examples, the significant digits are 5000 (1 - though the zeroes COULD be significant) = 508 (3 - everything between first and last nonzero digits) === 23.0 (3 - zero could have been omitted, must have a purpose) == = 0.05 (1 - zero couldn't be dropped, has no significance) = In general, significant digits are: 000xx0xx000 Between first and last non-zero digits ===== 000xx0xx000.000 Between first non-zero digit and last decimal ============ 000xx0x.x0xx000 Between first non-zero digit and last decimal ==== ======= 000.000xx0xx000 Between first non-zero digit and last decimal ======== Here's an interesting site with several links to explanations of significant digits: Significant Figures and Rounding Rules, Christopher Mulliss http://www.angelfire.com/oh/cmulliss/ Other answers in our archives dealing with this topic include Significant Digits http://mathforum.org/dr.math/problems/casey9.7.98.html Significant Figures and Scientific Notation http://mathforum.org/dr.math/problems/smith5.21.97.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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