Stanton D. answered • 11/09/20
Tutor to Pique Your Sciences Interest
Hi Ooyeon O.,
Yes, your calculation is correct up to that point (I didn't check your calculator's performance, but I assume it's OK as rounded and stated). You may have noted that you now have 2 legs of a right triangle, that should suggest a very old way of finding the hypotenuse!
One caution: it would be a very good idea to carry an extra decimal place or 2 through your calculation, THEN round to 4 decimal places. Otherwise a rounding "error" for b as stated could perhaps affect your calculation for c, making it wrong in the last digit (as rounded for an answer). This is a very common error in all sorts of student work, usually called "double rounding". It takes many other forms, too. Depending on what kinds of calculations are being done, you may need to carry one or more additional places.
You can, incidentally, see this kind of error displayed on a cheapie calculator, the kind that only does +, -, x, / , √, mem-store, mem+, and mem-recall. If you enter "9999...999" (however many places the display allows), hit √ , and then manually multiply by the result displayed, you will likely end up with "9999...998" . More sophisticated calculators can be similarly defeated by a number of nested "log" functions, inside nested "10^" functions, acting on an initial non-trivial argument. At some point, you lose precision, and hence accuracy on the return, as it were.
-- Cheers, -- Mr. d.
