Not a homebrewer but figured this question would be best posted here? I see most ABV on commercial beers having only 1 digit after the decimal but i've noticed some brewers put a second digit (e.g. 5.74). Do most brewers round it off or can you calculate that precisely? Probably a novice question but there it is
I go to the 1st decimal... 7.1%, 5.4%, etc... With hydrometer readings it will be +/- a few points anyway.
Pennies. Unless you're really able to eck out some money on them. Round to the nearest and get rid of em.
You can "calculate" ABV to any number of decimal places you want, if you're willing to ignore the rules of significant figures. Even if you follow them, you can generally calculate beyond one decimal point. But I suspect the reason most people report ABV only out to one decimal point is that it's usually only an estimate anyway (computed from measurements of original and final gravities...not a direct measurement of ABV), so they're hesitant to imply that it's an actual measurement by including decimal dust. Measuring actual ABV is fairly expensive. Or at least it involves equipment that most people don't have access to.
I want to point out that here, USA, the excise taxes are based on volume (barrels) only, but in other countries it is taxed both in strength (alcohol) and volume. It might explain why there are more decimal places. The UK is one country that comes to mind.
Isn't the tolerance on commercial beer something like half a percent, anyway? As in, a beer labeled at 7% can be anywhere between 6.5-7.5 without getting fined? Thought I heard that somewhere.
That is correct. You can measure the alcohol with an Anton Paar Alcolyzer, but only larger breweries can afford the price, about 30 k$ give or take a few thousand.
Scientifically, ABV can only be calculated to two sig figs, i.e., one decimal point, except for >10% ABV then skip the decimal.
I'm curious. Which input(s) do you figure (pun intended) limit the result to two significant figures?
As am I..... with a GC you can measure ppb levels of ethanol and get far more accurate that tenths of a percent
With my old eyes ,meniscal glare, and cheap hydrometer (hopefully Santa brings my error down) I am +- 2 points. If you figure there are two readings that is 4 points with a total difference of the OG at at about 50 points. That is +- 8% right there. And that is not the only error present just the biggest.
The calculation for ABV using a hydrometer is (OG - FG) * 131. A hydrometer reads specific gravity with accuracy to about a thousandth, e.g., 1.055. This one reading constitutes 4 sig figs. Right? Right. HOWEVER... when a second reading is subtracted from it beginning with the same 1.0(Xx), we are left with a factor that looks something more like 1.055 - 1.012 = 0.043. This latter number, in fact, contains only 2 sig figs. Thus, when multiplied with the mandated factor of 130-something with 3 sig figs, the lowest number of sig figs in the two factors prevails as the number of sig figs on the product, e.g., 2 sig figs and 3 sig figs multiplied always results in just 2 sig figs. Have a nice day.
It isn't a requirement that commercial brewers post any of the recipe information on the bottle or can. As for the homebrew community, I don't think we'd care so much to advertise the abv, as it's not an exact measurement with the equipment that most of us use. It'd matter more for our competitions, I suppose.
Interesting, thanks. I always thought that if you didn't round anything until the end, only the input with the least amount of significant figures was the one that limited the answer (ignoring intermediate steps). But following your rules (which I'll believe are correct...it's been a long time since school), why can't I write and compute the formula as... (1.055 x 131) - (1.012 x 131) ...and declare that the answer should have three significant figures? Ewww.
It always freaks me out when I see an American beer that doesn't have the ABV on the label. Pretty sure that's legally required in Quebec, as is the nomenclature "strong beer" for anything that's above (I think) 6%.
Hmm... let's think about this... Yes, 1.055 x 131 should give you a result with 3 sig figs, but since you want to save rounding for the very end, then hang onto an extra sig fig. So, keep the result with 4 sig figs. 1.055 x 131 = 138.2. Then repeat for the final gravity: 1.012 x 131 = 132.6. Then subtract: 138.2 - 132.6 = 5.6. You still end up with a result with only 2 sig figs, even when you save the rounding errors for last. Either way, it's 2 sig figs. Also, I didn't say this before, but the +/-8% error or whatever that others are reporting correlates to approximately 10% error which again means you've really got 2 sig figs. The whole choir is essentially singing soprano and alto, baritone and bass parts, each different parts on their own, but all coming together to sing the same song. It's a beautiful thing.
