With given:

estimate the absolute and relative error for and round both and the error in such a way not to lose any precise figures.

So my attempt looks like this:

We know the absolute errors for the three variables so we can calculate the absolute error for our w with:

The value of the itself for our variables is

Hence, the relative error for w is .

And as for the rounding: the "precise figure" is my translation as I couldn't find the exact thing I mean on Wikipedia. So by that I mean: we say that a rounded number has n precise significant figures if the absolute error of the number isn't higher than . So for example such that has 3 precise figures since . I hope it clears things up a bit...

So for the rounding: the absolute error is of form so we can round without loss of precise figures to the form of .

However, I don't have the slightest idea how to round the errors to not lose any precise figures. I mean: if I need the absolute error of a value to determine how many precise figures it has, how can I do it if I don't know the error of the errors?

Could you please guide ma and tell me if my thinking is correct and - if not - help me understand the problem? I heartily thank you in advance