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I'm not sure whether to round up or down to the nearest integer. The decimal is < 0.5, but the quantity refers to an amount of animals. So, is it common practice to round up or down when dealing with such physical quantities?

I've been taught to always round up when dealing with money, so I thought it would be the same in this situation.

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(differential-equations) is certainly not the right tag. I'm not sure if (soft-questions) is, but it's at least better. However, I'm not sure this is a mathematical question. I think it depends far too much on the precise situation you're working with, and specifically the non-mathematical details of it. – Alex Becker Mar 8 '13 at 3:42

I think the answer depends on context:

For example, if you are trying to determine how much food to stock up on to ensure that all the animals are fed enough, you'll want to round up (over-estimate).

However, if you are trying, say, to determine some sort of guarantee that the number of animals will be at least some particular number (contract with a pet supply store to deliver $x$ animals, then you'd round down to ensure you can deliver as agreed.) Or if you want to report some statistical claim about $x$ number of animals ....., then for the purposes of most accurately reporting this, if it needs to be an integer, would be to round down.

So the question is ambiguous, and we'd need to know how you computed a non-integer number to represent animals, and what the context in which the need to round up or down is necessary.

Mathematically, dealing with strict rounding, the convention is to round down for fractions x such that $0 \lt 0.5$, and to round up for fractions x such that $0.5\leq x \lt 1.0$

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I'm guessing that you'd want to round up in this case. I'm not sure what your problem is, but say the problem was... how many boxes do we need to fit all of the animals into them. And you got $32.3$ boxes, you'd want to take $33$ boxes then. This is a fairly bad example, but I think it shows the point. Hope that helps!

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