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I'm having a problem with biology--multiplying, and dividing uncertainties!?
I have a bio lab due soon, and i just realized that i can't find a true, comprehensive answer on what to do with multiplying numbers and dividing those with uncertainties. I keep seeing answers with percentageds, but that's not what i'm looking for.
This is what i need to calculate:
8.0 cm(± 0.1 cm) x 8.0 cm (± 0.1 cm) = 64.0 cm2 ± _______cm 2
then i need to add the answer to other similar ones (and if i'm not mistakken, in addition, we just add all the uncertainties for the final total uncertainties)
I dont want percentages and whatnot--just an explanation for the above multiplication and how it would look as division. Also, in terms of conversion from cm to mm, for example:
40.0 cm ( +/- 0.1 cm) x 10 = 400.0 mm
How would the uncertainty apply here?
PLEASE REPLY ASAP!
1 Answer
- Barry GLv 79 years agoFavorite Answer
The easiest way of estimating uncertainty is what I call "the mini-max method".
Apply the uncertainties in such a way that you get (1) the largest possible result, (2) the smallest possible result. Then the uncertainty is approx. half the difference between the two.
eg. 8.0 cm(± 0.1 cm) x 8.0 cm (± 0.1 cm)
min. = 7.9 x 7.9 = 62.41
max. = 8.1 x 8.1 = 65.61
half difference = 1.6 cm2, round to 1 sig. fig. = 2 cm2
so 8.0 cm(± 0.1 cm) x 8.0 cm (± 0.1 cm) = 64 ± 2 cm2
For the conversion: the uncertainty does not change size if you are multiplying by a number (which has no uncertainty)
± 0.1 cm = ± 1 mm
40.0 cm ( +/- 0.1 cm) x 10 = 400 ± 1 mm
NOTE: no ".0" at the end of 400 mm.
