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[MetalSlimeHunt]

But water's not an element.

I should've said "molecule", yes. 

You especially shouldn't have mentioned hydrogen, given that water is 33% hydrogen. And because its name literally means "water creating".

Water is either 67% or 11% hydrogen, depending of if you're going by atoms or mass, respectively.

While I got my formula reading backwards, I'm pretty sure it would be 66% by atoms, not 67%.

2/3
Or: 66.6666666666666666 Ad infinitum.

Rounding that to the nearest whole number is 67.

I have never seen a standard in which you are supposed to round up repeating numbers.

[Dutchling]

I have never seen 66.666.... rounded down o.O

[MetalSlimeHunt]

I'm not rounding down, I'm just not going into the decimal because it is commonly known that thirds result in repeating numbers.

[Dutchling]

Never see it happen that way either tbh.

Not saying it's wrong though.

[Descan]

I've seen it like 66.6667.

[da_nang]

I'm not rounding down, I'm just not going into the decimal because it is commonly known that thirds result in repeating numbers.

You're truncating it. However, truncated numbers usually don't work well in arithmetic in terms of accuracy e.g. 66% + 33% = 99% whereas 67% + 33% = 100%. Floating point arithmetic has to deal with this problem. Rounding it usually results in a smaller error.

[Urist McScoopbeard]

when dealing with significant figures, you round the number one decimal place past the most accurate calibration.

i.e. if you have a ruler that measures tenths of inches, and one edge of a piece of paper is a 0 and one edge is between 10.1" and 10.2" then you would round the length of the paper to 10.15".

following the rules of significant figures, in a sample of H₂O you would indeed have 67 hydrogen : 33 oxygen, assuming that is that the most accurate calibration on the measuring device was the hundred's place.

EDIT: and also by the rules of rounding 66.66666666 would be indeed be rounded up to 67, assuming that's where you're rounding to.

[kaijyuu]

Mostly moot discussion. If you care about precision, you likely won't be doing any rounding at all. If you don't care about precision, you likely won't care if the least significant digit is +- 1.

[da_nang]

Mostly moot discussion. If you care about precision, you likely won't be doing any rounding at all. If you don't care about precision, you likely won't care if the least significant digit is +- 1.

It's in percent. So least significant digit is +- 0.01

[Urist McScoopbeard]

you'll have to round because measuring instruments are only so accurate, I'd love to get the exact dosage for some medicine to administer, but a machine can only be so accurate, so you'll need to round to the point at which the machine can measure.

[MonkeyHead]

In the wonderful world of Physics, we round calculated values to the same number of SigFig as our instruments can measure... so 66.666 could easily be 67.

[kaijyuu]

you'll have to round because measuring instruments are only so accurate, I'd love to get the exact dosage for some medicine to administer, but a machine can only be so accurate, so you'll need to round to the point at which the machine can measure.

Aye, but at that level of precision, you probably don't care if the least significant digit is +- 1. 0.00001 mg less of medicine for someone isn't going to kill or save them.

You would probably care about +- 1 gram, but your instruments are more precise than that (as precise as they need to be).

[da_nang]

In the wonderful world of Physics, we round calculated values to the same number of SigFig as our instruments can measure... so 66.666 could easily be 67.

And if you're using a log scale, you never round to nearest integer e.g. pH-measurements.

you'll have to round because measuring instruments are only so accurate, I'd love to get the exact dosage for some medicine to administer, but a machine can only be so accurate, so you'll need to round to the point at which the machine can measure.

Aye, but at that level of precision, you probably don't care if the least significant digit is +- 1. 0.00001 mg less of medicine for someone isn't going to kill or save them.

You would probably care about +- 1 gram, but your instruments are more precise than that (as precise as they need to be).

Depends on how well-conditioned the system is, really. For instance, blood contains a buffer solution where the effect of acids and bases are decreased thus improving the condition number of the system. If the buffer solution wasn't there, however, the system would be ill-conditioned and a small introduction of an acid or base would have a much greater effect.

[Urist McScoopbeard]

you'll have to round because measuring instruments are only so accurate, I'd love to get the exact dosage for some medicine to administer, but a machine can only be so accurate, so you'll need to round to the point at which the machine can measure.

Aye, but at that level of precision, you probably don't care if the least significant digit is +- 1. 0.00001 mg less of medicine for someone isn't going to kill or save them.

You would probably care about +- 1 gram, but your instruments are more precise than that (as precise as they need to be).

agreed. Practical utility is limited, but important.

[GlyphGryph]

Medical Warning:
"Do not take Lunesta if you are allergic to anything in it"

Thank you for the WONDERFUL piece of advice, Lunesta!