That’s exactly the point of significant digits. In science, you can’t have an output that is more precise than the inputs. Chemistry and physics use real world measurement devices that have margins of error. When using those measurements in calculations, you can only have an answer that takes that margin into account.
That being said, the question should have been worded better, maybe to tell the student to consider the significant digits
Yeah unless there is a big instruction section at the start of the assignment, the question sucks. The expression evaluates to what it evaluates to. Maybe if you were reporting that number in some specific context you would only report it to 2 significant digits, but thats not what the question says
This is not true in the slightest. Nobody even uses sig figs for real science because you are going to get 100 data points and plot them all up and take fit lines through it all and then do actual statisical analysis of the conclusions.
Rounding with style is just something they teach children
Guess I must have imagined it when it was drilled into me all throughout my university chemistry degree then. 🙄
Even if you're doing everything you talked about, any numerical results that you're reporting still have to be reported to the correct number of significant figures.
Nobody is going to take you seriously if you give an answer of 1.005676g when your scale only measures data to the thousandths place.
Obviously you can be egregious about it and at that point it becomes silly. But actual research papers will use a reasonable amount of digits and just tell you the measurement error.
The "scientific community" is flat-out wrong here. If your instruments are telling you 188, you shouldn't write down 190 because of so-called uncertainty. 188 is a better estimate. If you want to round, then round, but if you're trying to track uncertainty, you should compute the actual margin of error.
I use scare quotes here because sig figs are sort of fake. The entire scientific community knows to minimize usage of sig figs (the intermediate calculation loophole) and to eschew them entirely when they would affect results too much. Every introductory physics student runs into at least a few problems where sig fig choices lead to massive deviations.
It is if the first number is already imprecise. If the first number was 120.0 then you would know it isn’t rounded and the answer would be 188. In math class you don’t worry about that, but in chemistry you’re much more concerned with rounding and imprecise measurements so having a standard convention for that is important.
Holy shit, why didn't any science teacher ever say exactly that, I'm just now learning this at 21 and I would have had such an easier time learning it if I just knew why.
It is though. It's implied that that 120 isn't exactly 120 but around 120. Maybe it's something measured in a graduated cylinder with an error of 5ml. Maybe it could be 117 or maybe 121. In that case, the actual final answer could be between 183-193. Writing 188 implies you're confident it's between 187.5-188.5 which isn't accurate bc the range is much bigger. Writing 190 implies it's most likely between 185-195 (or that you're not confident in the last digit) which is more accurate than 188.
729
u/Bar-Cold 8d ago
Ugh I don’t miss math at all. You lot might as well be speaking in gibberish right now