Regardless of your opinion on sig figs, '4' is one sig fig & '1200' is two. Its comparision to propagation of error is an entirely different discussion. It is clear in this discussion the numbers are not exact (infinite sig figs). The reason it is clear the number has one or two sig figs and is not an exact number is it is stated as such.
That said, yup. If they were exact (like 2*r*pi), it's a different discussion. Just as this is a derail on the parent discussion.
If your code correctly follows the rules for using sig figs, you can not get 4000 just as easy as 5000.
You would do something like:
Determine sig figs: 4 = 1, 1200 = 2
sig figs in result = 1
Multiply '4' and '1200' = 4800
To output the correct sig fig, round so you only have one sig fig
If you are stating a series of steps would yield 4000 just as easy as 5000, meaning you are saying something like add a couple & adjust for sig figs then add a couple more & adjust for sig figs & ect. then come to a final answer that could just as easily come to 4K as 5K, well, that wouldn't really be what was stated. What was stated included one step & one sig fig adjustment.
Also, depending on if you are following sig fig rules or not, your answer would be right or wrong.
Engineering answer: It depends. However in my example, 5000 is the answer. 4000 is not & can not be the answer because 4800 does not round to 4000 UNLESS you use some 'round to the lowest' type function. Which is not standard sig fig procedure.
4(1 sig fig) * 1200 (2 sig figs) = 5000 (1 sig fig & rounded up since 4800 is closer to 5000 than 4000)
4.0(2 sig figs) * 1200 (2 sig figs) = 4800 (2 sig figs)
As far as software using sig figs, well...if you are using real world measurements, you should be using sig figs. You can not tell from a general ruler if you are at 0.526876". You can tell that you are between 0.5" and 0.6", so you say 0.56" Past two sig figs, you would really be pulling that out of your bum. Therefore in all the calulations that use the 0.56", you can only have a max of two sig figs in the result. Anything more would rely on you knowing up to say 3+ sig figs in all the numbers used to get the result.
Point: The number of sig figs you have makes a difference in your result. Sig figs are generally used with real world measurement systems. Computer calculations may not fall into this category, but it would depend.
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Regardless of your opinion on sig figs, '4' is one sig fig & '1200' is two. Its comparision to propagation of error is an entirely different discussion. It is clear in this discussion the numbers are not exact (infinite sig figs). The reason it is clear the number has one or two sig figs and is not an exact number is it is stated as such. That said, yup. If they were exact (like 2*r*pi), it's a different discussion. Just as this is a derail on the parent discussion.
If your code correctly follows the rules for using sig figs, you can not get 4000 just as easy as 5000. You would do something like: Determine sig figs: 4 = 1, 1200 = 2 sig figs in result = 1 Multiply '4' and '1200' = 4800 To output the correct sig fig, round so you only have one sig fig If you are stating a series of steps would yield 4000 just as easy as 5000, meaning you are saying something like add a couple & adjust for sig figs then add a couple more & adjust for sig figs & ect. then come to a final answer that could just as easily come to 4K as 5K, well, that wouldn't really be what was stated. What was stated included one step & one sig fig adjustment. Also, depending on if you are following sig fig rules or not, your answer would be right or wrong. Engineering answer: It depends. However in my example, 5000 is the answer. 4000 is not & can not be the answer because 4800 does not round to 4000 UNLESS you use some 'round to the lowest' type function. Which is not standard sig fig procedure.
The broke broke piece of crap he is using is found here: http://en.wikipedia.org/wiki/Significant_figures
The rule in his example is:
4(1 sig fig) * 1200 (2 sig figs) = 5000 (1 sig fig & rounded up since 4800 is closer to 5000 than 4000)
4.0(2 sig figs) * 1200 (2 sig figs) = 4800 (2 sig figs)
As far as software using sig figs, well...if you are using real world measurements, you should be using sig figs. You can not tell from a general ruler if you are at 0.526876". You can tell that you are between 0.5" and 0.6", so you say 0.56" Past two sig figs, you would really be pulling that out of your bum. Therefore in all the calulations that use the 0.56", you can only have a max of two sig figs in the result. Anything more would rely on you knowing up to say 3+ sig figs in all the numbers used to get the result.
Point: The number of sig figs you have makes a difference in your result. Sig figs are generally used with real world measurement systems. Computer calculations may not fall into this category, but it would depend.