Understanding Significant Numbers: Rules and Exceptions Explained

[emc2cracker]

significant numbers??

Homework Statement

In my textbook significant numbers are numbers that we are certain of in any unit. There are lots of rules about what are significant numbers and what isn't, basically if you have lots of 0's in a number those aren't significant. And if you have a measurement that is approximated that is not significant either.

Homework Equations

The course is making me drop all non-significant numbers in coming up with solutions. However I am discovering by using detailed measurements with no approximate figures that my solutions are WRONG. For instance using a micrometer I can measure down to thousandths of an inch, as opposed to a ruler. It seems these rules are just assuming all measurements are approximations and a few numbers should always be dropped!

The Attempt at a Solution

I think this may be an outdated thesis from my textbook that is now 20 years old, have any of you studied significant numbers? I hope this isn't standard practice in computing solutions!

 

[Agent M27]

From my experience so far, you round your final answer down to the smallest amount of sig figs in the given information. Say a problem had 17.8g 12.54L and 1.230 ATM the final answer would be rounded to only 3 sig figs due to the 17.8. Hope this helps.

Joe

 

[jhae2.718]

It's not the most concise overview I've ever seen, but this http://en.wikipedia.org/wiki/Significant_figures should be a good starting place.

 

[emc2cracker]

Yeah the wikipedia is what I'm going to go by, this textbook turns it into guessing on almost everything. I don't like the idea of working with inaccurate integers, or omitting data. To me that places lots of doubt on any solution. I guess I can look forward to lots of this kind of thing studying a 20 yr old physics book... lol the joy of self study. Its really a good book otherwise, its a modern physics course. I'm studying it for my primer, next semester I'm starting my physics degree!

Who says 31 is too late lol, what's cool is my oldest daughter that is 11 yrs old is actually helping me and seems to grasp this stuff better than I do!

 

[jhae2.718]

Really, you should only round to the correct number of sig figs on the last step, so while you're working you should have accurate numbers.

 

[emc2cracker]

I don't like the idea of saying in 120,000 all the trailing zeros are not significant when one writes 120,000. they are significant. How am I to know if the person that wrote down the data simply omited the decimal point? As far as in the real world that rule shouldn't apply, I think people should take the numbers they are given at face value unless its plain as in ~1.5 we know its an approximation.

See I work as a machinist, to suddenly tell me I may be fabricating parts on guesses is insane! Especially when specs that I am given NEVER are written out in the way significant number rules spell out. I have made parts with 1/1000 of an inch error margin and they fit perfectly, if I used the significant number rules in my computation they would not fit.

I guess one has to know when this will apply and when it won't and use some common sense. It does say in my textbook that there are exceptions to the rules of significant integers.

 

[jhae2.718]

That's a valid point. Using low numbers of significant figures is best for applications where precision isn't as important, such as for giving a population. But you're not going to want to use only 2 sig figs on a part with high tolerances...

That said, after learning how to do them, I've never really used them.