How to calculate significant figures of a number? I got confuse as the number 28600 has 3 significant figure instead of 5. Anyone can explain?
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$\begingroup$ Have you read your textbook or the now-included Wikipedia link? $\endgroup$– Kyle KanosJun 17, 2015 at 13:52
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$\begingroup$ The number 28600 does not have any number of significant figures. It is an exact number. When you write a check for 28600 dollars, the bank will pay EXACTLY 28600 dollars or all hell breaks lose. When I order 28600 components from my electronics supplier, they will send me exactly 28600 components or I have a right to reject the shipment at their cost, which is why they have counting machines for this purpose. If you want to specify an accuracy for a number it's much better to do it explicitly like 28600+-1000. $\endgroup$– CuriousOneJun 17, 2015 at 18:34
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$\begingroup$ More on significant figures. $\endgroup$– Qmechanic ♦Apr 17, 2016 at 14:14
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2 Answers
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The number of significant digits in 28600 depends on what the error in the measurement is. If sigma = 15 Then we can write 28600(15) and there are 5 significant digits. If sigma = 1800 then we can write 28600 +-1800 and there are 3 significant digits. If sigma = 25000 then we can write 2.9(25)x10^4 and there are 2 significant digits. Significant digits are the work of the devil and cause much confusion. Calculate the uncertainty first and then you can calculate how many significant digits there are.
Jack
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1$\begingroup$ OP doesn't mention anything about error here. $\endgroup$ Jul 22, 2015 at 13:24
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$\begingroup$ This is incorrect. 28600 has 3 significant digits regardless what the uncertainty is (unless it is an absolute number). If the uncertainty is (15), then writing it as 28600 is inappropriate because that has 3 sig digs. It should then be written as $2.8600\times10^4$, which has 5 sig digs. $\endgroup$– JimJul 22, 2015 at 15:26
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$\begingroup$ If the error is large enough to affect the fourth digit, then the value only has four significant figures? $\endgroup$ Mar 14, 2021 at 12:50
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$\begingroup$ Is it correct to write “2.9(25)x10^4” if sigma = 25x10^**3**? $\endgroup$ Mar 14, 2021 at 12:52
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It have 5 significant figures, as the zeros are present on right hand side of a numbers .
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1$\begingroup$ Trailing zeros are generally regarded as insignificant, so it should be 3, not 5. $\endgroup$ Jun 17, 2015 at 13:54
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1$\begingroup$ Either your textbook is wrong or you misread it; trailing zeros are not significant. $\endgroup$ Jun 17, 2015 at 13:57
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$\begingroup$ Well, in the usual convention trailing zeros before the radix are not significant, but those after the radix are. $\endgroup$ Jun 17, 2015 at 21:45
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1$\begingroup$ I consider the number 28600 to be ambiguous with regard to significant figures. That is why it is best to use scientific notation for such numbers, such as 2.86 x 10^4, which clearly has 3 significant figures. $\endgroup$ Feb 28, 2016 at 3:23