My students and I have been irritated with a recent activity I designed that seems to occasionally mark incorrect an answer I would consider to be correct. I just discovered it comes down to a rounding issue. I understand rounding is just a convention - the way we as humans (or mathematicians) collectively agree to handle certain situations. I am simply wondering if the Desmos graphing calculator follows the same rounding convention all of you use?

This is a screenshot of how Desmos rounds some specific numbers. Is this how you round?

If this is not how you have always rounded numbers, is there anyone who has designed some kind of work-around to follow what I suspect is a more common convention?

In general, I like to compare the studentās answer to the exact answer within a given tolerance. So if I wanted them to estimate root(2), and Iām ok with it being up to 0.01 off, I would write something like:

@Daniel_Wekselgreene Thanks for your reply. My students are using the rounded number to then perform further calculations before coming to a final answer that is checked for correctness. Introducing tolerance for the rounded value creates numerous possibilities of ācorrectā final answers, if that makes sense. But your use of the absolute value gives me an ideaā¦

Since the calculator rounds positive numbers the way I would expect (only negatives are different than the convention I usually follow), I think I can use the graphing calculator and CL to ācheckā if the original (unrounded) value is negative or not. Separately, Iāll have it take the absolute value of the number before rounding. Then I will have an expression in the calculator that āre-appliesā the negative sign after rounding the positive value. In the CL Iāll just have 1 final answer based on that value if the ācheckā returned a positive number and 1 final answer if that ācheckā found a negative number. I think that should workā¦?

Iāll just have to remember that Desmos doesnāt round as I would expect with negative numbers moving forward. Thanks again for your reply that prompted an idea that should work!

I never really considered it much, but there are apparently 6 different ways to round. Hereās a thread on stackexchange. Apparently most computer rounding is to the nearest even number!

Looks like Desmos uses the convention of rounding halves āupā or the positive direction, while youāre looking for rounding away from 0. You could make your own function.

r_{ound}(n, d) = \sign(n)(\round(\abs(n),d))

There may be someone more knowledgeable at support.desmos.com which handle the graphing calculator.