(Disclaimer: I have ADHD and am completely useless when it comes to math. So please forgive me for being super-stupid on the subject.)
To my understanding, Mathematics are seen as completely logical. Which I don’t have a problem with except for when it comes to one certain thing in math that I just can’t make sense of as being considered logical:
Rounding of decimals.
To my understanding, the rule is that when you have a decimal that is 5 or higher, you round up. If 4 or lower you round down.
Two things that I don’t understand about this:
1. When you round up, you magically pull value out of the air that wasn’t there to begin with, and do the opposite when rounding down. How is this considered logical?
2. The rule isn’t applied universally. I’ve seen cases when, for example, making store purchases, no matter how low the decimal, it is rounded up and not down.
I appreciate any help you guys can give. Thank you in advance for the assistance! <3
In: 6
I don’t think anyone’s quite addressed the question yet. There’s a couple of things going on.
First, rounding is *convention*. It doesn’t make sense to talk about it being “logical” or “not logical”. It’s something we collectively agree to do in certain situations, not something you can prove.
For instance, I can prove, beyond a shadow of doubt, that there are infinitely many prime numbers or that it’s impossible to construct a regular heptagon with a straightedge and compass. These are mathematical *theorems*. I can’t, on the other hand, “prove” that 0.63 rounded should be 1 instead of 0.6, because we haven’t given rounding clearly defined rules. This is by design: We use it in whichever way is most convenient at the time.
Note that if I instead talk about “rounding to the nearest tenth”, then *that’s* a rigorously defined operation and I can start making factual statements about it. I can say that rounding 0.63 to the nearest tenth is 0.6, not 0.7 or 1.
I can also say that “rounding 0.63 gives 0.6”, and ask you to infer from that statement that I *meant* “rounding to the nearest tenth”. If you then turn around and say “0.63 rounded is 1”, you’re not *wrong* for disagreeing with me, we’re just using ambiguous language in different ways.
Second, math is *abstract.* I encourage you to let go of the idea that numbers embody “value”, or that there was anything “there to begin with”. Rounding is just another operation that takes a number as an input and spits out another number as an output, no different from, say, adding 1, or squaring, or taking the cube root.
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