Monday, September 29, 2008
Sig-Fig SCHMIG!
There's an old saying that goes like this: "A chain is only as strong as its weakest link." How might this adage be applied to the concept of significant figures? Why is reporting measured quantities with the correct number of significant figures considered to be an integrity issue in science?
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This saying can be applied to a significant figure because a significant figure is only a significant figure if all of its digits are present. Reporting measured quantities with the correct amount of significant figure is considered to be an integrity issue in science because pin-pointing precision in science is very hard to do. If everybody could be precise to the point where everything fit together like a puzzle, then science may not be the complicated subject it is today.
This saying is true to Significant Figures because your answer can only be as precise as your least precise measurement. If your ruler only measures centimeters, and not milimeters or any smaller incriment, your answer should not have any figures past your estimated second figure. This is an integrity issue because if someone said that the length of the num chucks was 37.346623453 centimeters, but their ruler only measured to the nearest centimeter, 8 of those digits would be considered BS.
This saying can be applied as a significant figure because if you gathered a bunch of data, the data is only as accurate and precise and your least accurate and precise piece of data. This could be an integrity issue because one might put down unnecessary digits past the decimal point, creating a less precise number.
This can be applied to Significant Figures because just like a weak link, a gathered amount of data is only as accurate or precise as the smallest figure. This could become an integrity issue because many measuring instruments round off the measurement at some point or another. By doing this; the answer simply is not correct. The smaller the increments on a measuring tool; the more accurate data will be found.
This is applied to significant figures because of how un-precise we can actually be. In class we did a group exercise where we had to measure a note card, but each with a different ruler as far as increments of measurement (centimeter, inches, etc.). We then would record theses figures and find an average for each ruler (A.B.C.D). It showed us how no matter how precise our answers seemed to have been, no matter what you can always go smaller. So when we rounded our answers, we could have in fact found a ruler a bit more precise and achieved a more accurate result. Then again we can always keep getting more precise, so actually having that precise of an answer is very rare, thus make it the weakest link in the chain.
The adage can be applied to the idea of Significant figures because it is the least precise and accurate measurement that makes a measurement truly accurate. If you cut a measurement short a few digits (and almost every calculator does this by rounding), then the measurement cannot be 100% accurate. This can be an integrity issue because when an answer is cut short like that, it cannot be called completely accurate, or that statement is false.
There's an old saying that goes like this: "A chain is only as strong as its weakest link." How might this adage be applied to the concept of significant figures? Why is reporting measured quantities with the correct number of significant figures considered to be an integrity issue in science?
Honestly, I am not 100% sure how this adage applies to the concept of significant figures, I just can't see it. When someone says "a chain is only as strong as its weakest link", they usually are talking about a team. For example, if you are in a team competition where everyone has to finish for your team to win then you are only as strong as your weakest player, I really do not see how this applies to the sig figs.
I know that sig figs basically tell us that you cannot go smaller in number than what you are measuring with. For example, if you are using a ruler that is 12" (and only has " marks) and you measure something that is 8.4", something that is 8.5, and something that is 8.7, if you do the math on a calculator, the average will be 8.5333 (incorrect!).
Sig figs tells us that we measure through the least count plus one doubtful digit. If we report more than one doubtful digit, that does not show integrity because you can't know if something is 8.53 when you only can measure one decimal place.
I still have no idea how this connects to that adage of the weakest link.
"Chris" = Chris Stone I was using the wrong account
This saying ties in with significant figures because collected data is like weak links. The data itself is only strong if the numbers collected to form the data are all correct, too. Reporting measured quanties with the correct number of significant figures is an integrity issue because when you round a number, it is not correct.
This saying makes sense when talking about sig figs because your measurement is only as precise as the least count of your measuring device. You can only have one doubtful digit beyond the least count. This is a problem with integrity because if you go past that one doubtful digit then you are just GUESSING what the measurement is. You are lying about the measurement if you have more than the one doubtful digit.
This saying easily describes the importance of a correct significant figure. Obviously, if you collect data from an experiment, and have the wrong significant figures, they will result in incorrect answers. More importantly though, when one measures something, and adds figures that are not accurate at all, and are simply a guess, they are trying to make up significant figures that also will possibly create an incorrect answer. They relate to the chain saying because if a number that is totally inaccurate is put into the equation, it will ruin the whole experiment, no matter how small of an addition it may seem.
This adage can be applied to the concept of significant figures because a significant figure is a value read from a measuring instrument that has been expressed as a number. A significant figure includes all digits as read from the instrument plus one doubtful digit. This doubtful digit is an estimate that will be a fractional part of the least count of the instrument. The doubtful digit estimate is made in order to leave room for error when making measurements, because every measurement has an element of uncertainty. The issue of integrity comes into play here because a significant figure requires a proper estimate and ONLY one doubtful digit, if there is more this is considered bad science, and ultimately if there is more than one doubtful digit the digit preceding the last one is assumed as correct; this would obviously be bad science. So, in relation to the chain in the adage, a value is only as strong as its significant figure: meaning that a values significant figure is its room for error and the doubtful digit must be properly estimated and recorded for a value to be "strong.
This saying can be applied to significant figures because if one does not get the significant figures of a prediction correct then the prediction is weak. So if ones prediction has many decimal places in it, it is a weak prediction. This can be considered to be an integrity issue because if there is a large amount of numbers after the decimal place it must appear in past measurements that lead up to ones prediction if these extra numbers are not evident in the past measurements then that is bad science!
This saying applies to significant figures because the "weakest link" is congruent the doubtful digit in a measurement. A measurement can only include the significant figures plus one doubtful digit. If there is more than one doubtful digit in a measurement than the measurement is a guess and not viable to use in a data set. So, the weakest link of a measurement is the doubtful digit, meaning that without the doubtful digit the measurement wouldn't be as precise as possible and also unable to use in a data set because it could be a possible outlier. Using the correct number of sig figs is important because if there were more digits than necessary, it would be wrong because it's a guess.
This expression can be applied to significant figures in terms of accuracy and precision. Significant figures are dependent on the measurements included when determining the Sig-Fig, much like how a chain is dependent on its links. If one of the measurements strays far away from the others, then that could impact the accuracy or precision of the figure. The Sig-Fig can only be as precise as its farthest deviation, or its 'weakest link'.
This saying can be applied as a significant figure because if you do an experiment, the data is only as accurate and precise as your amount of significant figures. This means that all digit as read from the instrument plus one doubtful digit. the measurement tool that you are using defines the amount of significant figures and overall how accurate your experiment is going to be. For the integritypart- I think that scientist have to be honest when they mesure in experiments because a mesurement with too many doubtful digits is bad science!
-Haley
It is important to the idea of significant figures because, you that you can only be as accurate as the smallest measurement i.e. the weakest link. So if one try’s to go beyond the smallest amount they can measure then they are going into the realm of BS.
This saying can be applied to a significant figure because if one has gathered together large amount of data, it data is only as accurate and precise and one's least accurate and precise piece of data. One might put down unnecessary digits past the decimal point, creating a less precise number but all that one would need is one doubtful digit.
Recording a measurement with the exact amount of significant figures can be a problem to some people because it is imposible to know how accurate you actually are. It is imposible to know this because a ruler isn't capable of displaying the smallest unit of measure because that unit is infinite. I personaly do not see a problem with significant figures because it is just an assumption. And everybody needs to see that science is always made of assumptions and there is never a discovery that we know for sure is 100% correct. I believe that the people who see this as a problem are not looking at science the right way.
The saying makes sense when talking about sig figs because measurements are only as precise as the least count of the tool you are using. You can also estimate to the next level past the least count. This could be an issue in integrity because you cannot know for sure the next digits beyond your estimated number.
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